Oh, I love name threads!!!! I keep waiting for a name section here at MDC.
Ok, my take on it is this - four letters, two syllables. (Because you have two with one syllable, and only one with two syllables.) No names starting with J, A or L as you already have those, and I think you either have to go with all the same first initial, or each their own.
As cute as Nora, Cora, Zora are... Jade, Adam, Luke and Nora. Am I the only one who thinks Luke and Laura from General Hospital?
Not terrible but there must be something else.
I think your girl name is a bit more unique than the boys' names - so I wouldn't go with Mary or Lynn or Emma or Sara. I'd try to pick something with the same "uniqueness" as Jade.
You also have two initials that are consonants, and only one with a vowel. So I like:
Iris - doesn't feel as strong as your other kids' names
Eden - not my favorite with an Adam in the mix, but sounds good with others
Opal - really love the theme connection, sounds great with the others
Asia - feels like it fits the theme too
Second tier (breaking my vowel or syllable rule) would be:
Ruby - theme connection
Tori - seems too "cutesy" to go with your strong kid names
Wren - really love this a lot!!!!
Maya - seems not to go as well
Sage - love the way it sounds with your kids' names
Gwen - LOVE this one!!!
Kira - like the name but not as much with your others
Bryn - love this name but I like it spelled Brynn better...
Bree - think this sounds good with your other kids' names