I'd pronounce it El-eese, sorry! And I think that Elize is like Eliza without the a... if you want it pronounced El-eeze I think you'd have to spell it phonetically to prevent people saying it wrong, so like Eleeze, but the spelling isn't as pretty lol!
It's the trouble with some names, and I'm trying to avoid them as don't want to constantly correct people!
I see it's a slightly older post, have you had any more thoguhts on it recently? x