Companies have track records. Simple question, what happened to the company's previous consultant? or to put it another way, what is the least flattering answer to why did they call you instead of someone else?

Decide if this client is worth associating with in terms of future work. Are they worth going to war with against Google?

You already have a suspicion that a perma-ban could be in the cards.

If their account is flagged, you can't help them. If Google isn't going to help, you can't help them. You can't help them if their problem can't be fixed.

It might be time to call your lawyer and figure out how to walk away...there's a Kenny Rogers song about it. Good luck.