Sounds like a messy gig you've got there.
Tempo management is a real pain, but I dimly recall that Sib allows you to include audio tracks, just as you can include a video track with audio.
If the tempo wanders wildly, I reckon you'll just have to take it in sections as you would with film cues. Then stitch it all together at the other end.
Sorry, but I just don't think you're going to get the sync you want automatically. Or rather, I think that you'd waste more time trying to fix up a sync solution than doing it by hand.
If anyone more wizardly wanders by in the meantime, I'd love to hear from them. But you've got to get on with this, right?
And look on the bright side. It's an incentive to work fast and trust your first instincts. That's often where your best work comes from anyway.
PS Here's a link to my review of NotePerformer, with an example:
https://jasonlyonjazz.wordpress.com/.../note-perfect/