I think with the longer middles of Elizabeth & Josiah, a longer middle could be the go. I also think a longer one balances the gender neutrality of Emery. I like Sophia best - and it’s in a subtle way a nod to Josiah as well.
If you’re going short though, I prefer the flow of Jane. It’s probably the easiest to say of the three.
But if you want some other ideas:
Emery Anastasia
Emery Charlotte
Emery Madeleine / Madeline
Emery Catherine
Emery Georgiana
Emery Camille
Emery Seraphina