Clark – I'll have a detailed reply to your question:
"So the workflow would be something like..." but it'll have to wait half a day or so.
In the meantime, some other folk here may fill you in on recording logistics. The good news: it's easier than it sounds.
The bad news: getting the gig in the first place ... 
... but ... more good news: your stuff sounds great! (imho)
cheers – jada
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1st April: sorry, really flat out. Hope to address Q more fully soon.
Basically, you use the "midi" setup at the sync'ing stage. The synthesized tracks might be all you need (or: all the budget will allow). Generally, live instrumental parts are recorded as overdubs (with either the synthesized track, or click, or both, in the players' cans).
gotta run – jada – that
sync'ing feeling