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To complete the circle of sibling initials, this one would have to be Elke Sibella or Eirlys Saskia... :-)
Hmm... Shakespeare: Cordelia Juliet. Floral: Juniper Delphine or Zinnia Delphine. Greek: Xanthe Cressida or Ariadne Sibella. Most Holy: Ariadne Agnes. (I actually quite like the combination.)
This is fun, but I'll stop there. The point (if there is one <grin>) is that the associations and significance of the names can help to find the combination that speaks to you most.
Don't use Senna. It's a stimulant laxative (the active ingredient in Ex-Lax), and anyone who solves even the occasional crossword puzzle will know that.
I agree with Natasha-Rhiannon: flow with middle names doesn't matter. If there are two candidates, you can use it as a tie-breaker, but otherwise, worry about how the given name and surname work together, and maybe about whether the initials spell something unfortunate (although even that can be worked around by simply strategically including or omitting the middle initial in the monogram).
All that said, I think the flow of Eliana Reyna is lovely and melodic.
Avery is given to about four times as many girls as boys nowadays, so given that middle names mostly disappear in everyday life, you're probably OK.
However, I happen to remember that Avery is a form of Alfred, so yes, it's too masculine for my tastes -- but then, I don't like boy's names on girls, period. (It's perfectly OK to give a girl a boy's name, but heaven forfend the other way around. Think about what that says about how our society values femininity. Do you really want to tell your child and all her friends that boys are better?)
Any interest in Averil? (Yeah, I know, it'd be an uphill struggle not to have it mistaken for Avery, and nobody knows it, so the fact that it's a historically feminine name wouldn't help one iota on a practical level...)
I've had people ask how to spell Julia and David. Asking about the number of Ts in Greta falls into the same category.
You characterize his taste as preppy; based on Cassius and Julian, yours could be characterized as classicist. Preppy names tend to be either English surnames-as-given (Blake, Logan, Prescott) or given names that are also familiar as English surnames (Chase, Asher, Percy). Perhaps some overlap could be found by looking for English surnames (especially unmarked patronymics) with a classical/Roman feel or association?
Ambrose; Atticus; August or Austin; Calvin; Evander; Horace; Jude; Lucian; Macsen, Magnus or Max (or Maxton or Maxwell); Quintus; Terence.
It's not the name that's teased, it's the child. Put certain personality types and learned behaviors together, and they'll find something to tease about. (Or to put it another way, _every_ name has teasing potential.) If you're extremely worried, I suppose there's Minna, but I really don't think it's necessary.
I think the default American pronounciation of both Mina and Mena has the first syllable like "me", and Mina is associated with the very "catch-all European" Wilhelmina (and a bunch of fairly esoteric Italian-ish things like Jacomina and Fermina), so I think the overall impression from both spellings is "European-origin girl's name". Ximena just explains why some people think specifically "Spanish" -- but those people will generally be in the minority.
To honor a Philomena, I'd definitely go with Mena.
As for the "5 Mias" worry: as I've said fairly frequently, this is statistically exceedingly unlikely in today's fractured naming landscape. I know one Mia, age 12, and there are a grand total of two of them in last year's student directory (K-5, 400-something students). You may still end up with multiple children with the same name in a class or grade level, but the nationwide (or even statewide) statistics can't predict which ones they'll be. (In the aforementioned directory, the most common name is Ryan.)
I think it depends highly on how destructive the storm ends up being. If (God forbid!) it ends up a Katrina-scale disaster, then usage of the name will plummet. If it only causes property damage (even if severe), then the name will probably (continue to) go up in usage.
I know two families who live directly in the projected path (you and our former neighbors who moved down there this summer). I hope it turns out less bad than they're currently saying.
(I'm looking into the moderation list, but in the meantime...)
I agree with Molly: the surname is much less important to the middle name choice than it is for the given name. Austin Sterling Helm is perfectly fine. (So is Austin Starr Helm, although there's a bit of comic book hero possibility there.)
Mena is ambiguous on pronunciation: first syllable like "may", "me", or "meh"? This need not be a deal-breaker: Mia was ranked 6th last year despite having at least two possible pronunciations (MEE-ah or MY-ah).
My personal preference is to name her Philomena and use Mena as a nickname. (It doesn't hurt that I think Philomena is a great name.)
I think people get a "Spanish" feel from Mena because there are really only two traditional names that it's short for: Philomena/Filomena, and Jimena/Ximena.
Liam didn't make it into the top 10 until 2012. Are those four Liams kindergarteners?
The point is that the numbers do not predict name experiences any more, especially not the nationwide numbers. If your sister taught at my daughter's elementary school, she'd be more likely to end up with a classful of Ryans than any other name. This unpredictability will only increase among your child's age-mates: in 2017, no boy's name was given to an entire percent of boy babies born. Think about it: no name reached one in a hundred, nationwide.
Don't worry about the rankings and percentages. They will not determine your son's experiences with his name.
Talan is an old Cornish masculine name (https://www.s-gabriel.org/names/tangwystyl/bodmin/celtic.htm#Celtic), and I believe it's pronounced more like "talon" than like "tail+en".
The only Archer I know is a collie, but it does fit both your sibset and current fashions in boy's names. The only problem is that combined with your surname, it makes for a rather martial name: head protection for a guy with a bow and arrows? I like Austin better, both in general and with your surname.
People or charities that manage feral cat populations also use microchips (in addition to the ear clip to signal "already spayed/neutered"). That way they can keep the cats at least mostly up-to-date on rabies shots.
I like the link between the middle names (both are associated with the concept of "life"), but I agree with other commenters that the combination Taylen Lively fails to signal "feminine" the way Elle Vivian clearly does. This could be a source of sibling friction, down the line -- or your daughters could fail to notice it until they're 40.
Other names associated with "life": Zoe, Eve/Eva, Enid, Liv(ia).
Traditionally-feminine names that bear some resemblance to Taylen: Thea, Tamar, Talia, Helen, Marlen, Kayla.
Surname-names are very much Not My Style, especially masculine patronymics (-son, Mac-) on girls, but I don't mind them nearly so much if they're surnames from the family tree.
If parents name their daughter Madigan because it's grandma's maiden surname, I'm good with that. If they choose it simply because they want a "unique" formal name for Maddy, I cringe. This is especially true for very-masculine surnames like Abbott and Emerson.
Twofer: name the cat Mary W. Shelley -- with the W. standing for Wookie instead of Wollstonecraft. Cats can deal with having multiple names almost as well as children can.
I've mostly had cat-named cats; the exceptions were Blanka (though my dad insisted on calling her Szöszi "Blondie") and Bence (/BEN-tseh/, originates as a form of Vincent, nowadays used as a nickname for Benedek = Benedict and Benjamin). (The latter was due to a children's song where Little Bence gets in trouble for climbing into the _kemence_ [bread-oven] and getting all sooty.) None of the names are at all creative, really: Bütyök ("knob"), Mici/Mica (rhyming nicknames based on _cica_ "cat"), Gombi (diminutive of "button"), Nyavi (based on the verb "to meow"), Buksi (endearment meaning "big head", like a baby), Buddy/Öcsi ("little brother"), Missy/Hugi ("little sister"), and Zap (a Lois McMaster Bujold reference). My husband had Smudge (a tiny black cat) and Amber (a very large pale orange tomcat).
Mostly keeping to names in use in European languages:
Ebba, Becca, Rebecca, Boudicca, Edda, Hedda, Annukka, Henriikka, Marjukka, Rebekka, UlriikkaAdella, Annabella, Antonella, Arabella, Ariella, Bella, Briella, Brunella, Calla, Camilla, Carmella, Christabella, Cilla, Cinderella, Csilla, Cyrilla, Daniella, Della, Donatella, Donella, Drusilla, Dulcibella, Ella, Estella, Estrella, Fenella, Fiorella, Gabriella, Gisella, Gizella, Graziella, Gunilla, Idella, Isabella, Izabella, Janella, Joella, Kalla, Kamilla, Lilla, Llewella, Louella, Lucilla, Ludmilla, Luella, Mabella, Marcella, Mariabella, Mariella, Marinella, Maristella, Milla, Mirabella, Mirella, Nella, Nigella, Noella, Olalla, Ornella, Pamella, Pernilla, Petronella, Petronilla, Priscilla, Prunella, Quintella, Raffaella, Rilla, Rosabella, Rosella, Rossella, sabella, Scilla, Sibilla, Sibylla, Stella, Sybella, Sybilla, Talulla, Ulla, Ursella, Willa, Zella, ZillaEmma, Gemma, Imma, JemmaAdrianna, Alanna, Anna, Arianna, Breanna, Brenna, Brianna, Bryanna, Corinna, Danna, Deanna, Dianna, Donna, Fenna, Georgeanna, Gianna, Giovanna, Glenna, Gunna, Hanna, Henna, Hosanna, Ioanna, Iohanna, Ivanna, Janna, Jeanna, Jenna, Joanna, Johanna, Johnna, Jonna, Julianna, Keanna, Kenna, Korinna, Ladonna, Leanna, Luanna, Lynna, Madonna, Makenna, Marianna, Marzanna, McKenna, Minna, Monna, Morwenna, Nanna, Nonna, Osanna, Panna, Pollyanna, Ravenna, Reanna, Rheanna, Rhianna, Rihanna, Rosanna, Roxanna, Sanna, Saranna, Savanna, Seanna, Shanna, Sienna, Sousanna, Susanna, Suzanna, Tatianna, Tatyanna, Tianna, Vanna, Wynonna, Yanna, Yulianna, Zanna, Zavanna, Zhanna, Zsuzsanna, ZuzannaFilippa, Giuseppa, Philippa, Pippa, Azzurra, Cearra, Cierra, Kiarra, Kierra, Sarra, Sierra, Terra, TierraAgnessa, Alessa, Alissa, Allissa, Alyssa, Anissa, Carissa, Charissa, Chryssa, Clarissa, Elissa, Janessa, Jenessa, Jessa, Karissa, Larissa, Lauressa, Laurissa, Lissa, Lyssa, Marissa, Melissa, Narcissa, Neassa, Nerissa, Nessa, Nissa, Nyssa, Odessa, Rossa, Sassa, Tessa, Ulyssa, VanessaAnnetta, Antonietta, Benedetta, Bernardetta, Bernetta, Birgitta, Brigitta, Britta, Carlotta, Charlotta, Claretta, Concetta, Coretta, Crocetta, Detta, Doretta, Elisabetta, Etta, Fiammetta, Floretta, Giosetta, Giovannetta, Gitta, Giuditta, Giulietta, Gretta, Harrietta, Henrietta, Isotta, Jacquetta, Janetta, Jetta, Joetta, Julitta, Jutta, Lauretta, Loretta, Lotta, Lucetta, Margaretta, Marietta, Maritta, Marjatta, Marketta, Martta, Melitta, Merletta, Netta, Nicoletta, Nikoletta, Odetta, Orietta, Pauletta, Piritta, Reetta, Rhetta, Riitta, Rosetta, Simonetta, Violetta, WiolettaCondoleezza, Santuzza
Can you get your family on board with Artemios? It's a Greek masculine name derived from the name of the goddess. Other masculine variations: Artemas, Artemus, Artemidoros ("gift of Artemis"), Artem, Artemio, Artemisius, Artemon.
But you're right that it's the child who is bullied, not the name, or the glasses, or the hand-me-downs.
There's also nothing inherently feminine (or masculine) about the sounds of Artemis; Aramis is one of the Three Musketeers, Semiramis was a queen. And of course Artemis Fowl (II) is male. So if Avery and Madison can be top-20 names for girls, why not a boy named Artemis?