FFXII / Vagrant Story: What if Balthier ended up in VS!era Ivalice, rather than FFT!era?

Balthier and Sydney seem like they would have a lot in common: maybe too much to get along smoothly to start with-- but I'm curious what would happen if they had a common goal they needed to work together towards (an Occuria in VS!Ivalice? Getting Balthier back to his "proper" time period?)

I'd like gen between Sydney and Balthier for preference, but mostly because I wouldn't exactly say no to background Sydney/Hardin if you were so inclined. ;)