The only thing I can think of involves life insurance, murder and a pact of silence.

Or Pluraleyes: http://www.redgiant.com/products/all/pluraleyes/

My God, I've had some bad beats but this sounds like someone crafted a nightmare specifically for you.

I'm guessing when they ask you what you think, they don't want your artistic input, they just want you to hold them. Reshoots are out, financially, right? Keep it technical and financial and within your department. Unless the audio is fixed, something that can be done with minimal (if tedious) effort, then the sound issues will make it unreleasable, guaranteeing no return on investment. If the sound sources are fixed, you can do your job and they can release it. You just upped their return from zero. You're a hero.

If you have to throw good money after bad, better make it the least amount for the most return. If everyone including Choppy is made aware of his role in the clusterfuck, shame and fear should make him more pliable. Getting Choppy to sit long hours syncing, because of his failures, is a low investment. He also gets punished for his incompetence. If Choppy's too slow/incompetent to get the job done, suggest they take some of his fee to pay an intern to do it. His shit-eating grin of agreement will be informed by the terror that, due to his incompetence, they may never release the film.

Sync the clips, post the audio, get the fee, watch them take the loss again, shake your head. Then send them to me. I have an amazing script that's perfect for April, shooting in the Spring. I just have to write it this weekend.