I'm curious what you'd like to do next. You could probably have a great career doing these sorts of turnarounds repeatedly across companies, maybe even as a consultant, but would you want to?
It's hinted by the C-level that if I can pull this off, it would be nothing short of a miracle. I'm pretty sure I can negotiate salary, education, bonus, and what not if I can pull this off.
As far as next, I've thought about that. It would be funny to call myself a turnaround specialist. This would be quite a remarkable feat, but I really don't know if I would have taken this job if I knew what a mess this was...
Do this up front. Do it as soon as you possibly can. You will lose a huge amount of negotiating leverage if you "wait until you show them". I cannot stress this enough.
I am not sure how much you could negotiate but you can have something like that and being metric based. X% customers happy, x% rating change, x% customers retained when they were close to leave. Then you make the math of the revenue and profit and it’s hard to say no.