I like Eamon Henry and Eamon Daniel.  Eamon as a name takes a little educating for most Americans and I think Alexander and Harrison are a little too long and weigh it down. Harper is not really my sytle, but is very popular right now, mostly for girls.

For you girl names I like:

Ella Joy (plus she could go by EJ- cute!)

Marah Joy and  Mila Joy the best.

I like the name Faith- it's sweet and simple, but I think Faith Joy would be too much meaning and Faith Lee blends together too much. I prefer Maggie as a nickname for something longer- Margaret, Magnolia, Magdalena. Hailey, to me, is very 1990s, I knew several Haileys of that generation who are now twenty somethings.

Jillian I like but again I don't think it flows with your middles.

Jillian Lee is a lot of L sounds and Jillian Joy sounds a bit cartoonish to me.

Good luck with your naming process.

I like Eamon Alexander, Eamon Henry and Eamon Daniel.  I think they all work well with your last name. If I had to pick I might go with Henry but they are all good options. Harrison is nice enough but I think the others are better. Harper is more trendy/leaning girl so unless it has special meaning I wouldn't use it given the other great options.

Jillian/Gillian doesn't go that well with either Joy or Lee. Joy is slightly better. I quite like Gillian and it sounds nice with your surname. You could do Jillian Faith?

Faith definitely doesn't work with Joy and Lee sounds a little funny too. I would maybe see if you could find another middle name if you are going to use this. Maybe Faith Ella or Faith Mila?

Ella Joy sounds great. Ella is a little more popular than some of your other options but is still a sweet name

Mila Joy is great. I think Mila Lee is too much 'L' sound for me.

Marah Lee and Marah Joy both sound good, it's hard to pick between them.

Hailey Joy is better for me than Hailey Lee as it is less L heavy. I find Hailey a bit dated but it's a nice name.

I think my favourite of your girls names are Mila, Marah and maybe Gillian/Jillian. 

I like Eamon Harrison, Eamon Henry & Eamon Daniel the best.  Of those 3, Eamon Henry is probably my favorite.  Mmmm.....or maybe Eamon Harrison.  

Of your girl names, my favorite is Gillian.  However, I agree with previous posters that it doesn't work well with Joy or Lee.

I also don't think Faith works well with Joy or Lee.

Maggie I really like as a nickname, but not as a given name.  If you really want it to be the given first name, then my vote would be for Maggie Joy.

I really like Ella Joy and Mila Joy is OK.  I don't think Ella or Mila work well with Lee.

Marah Joy or Marah Lee are both very good, I think Marah Joy would be my favorite of all your candidates and I think it would be a great sister name for an Eamon.  I'm assuming it's said like Maura?

Hailey seems to be the outlier when I consider it next to your other girl names in that it does seem a bit dated. I don't think Lee works with it at all, but Hailey Joy would be OK.

Thank you all so much for your ideas and impressions of the names! I really appreciate it. I think Eamon Henry and Marah Joy are our current #1 picks. 

Thanks again!