Great, thanks everyone. You've been such a huge help for me during this process. We'll see where my husband and I land eventually - time to ponder and think things over for a while!
I know an Annika who pronounces it like Hanneke without the H. It's up to you. I think the majority pronunciation in America is with the short A, but I like the other much better.
Your husband has very good taste actually, it's just different from yours. I tend to like shorter, spunkier names too, but I like the idea of giving one of your favorites a more feminine spin and see how he likes it.
You like Eliza, he likes Elizabeth, that seems like a great option to me. Elizabeth nn Eliza. Gorgeous.
I prefer Marin to Marina. Marin is a chic place name.
The only Annika I've ever met pronounced her name to rhyme with Hannukah, but people pronounce it both ways