My thoughts are in line with this. Are you (honestly) being hired or promoted to fix this mess, or to keep things running?

If the former, has the incredible scale and scope of this been properly identified, addressed, and acknowledged? Are you guaranteed anything near the resources to (try to) accomplish this (including your own time, without traipsing far into overtime)? Is the current state documented sufficiently to obviate any and all future attempts to blame you?

If the latter (more likely, I suspect), well... I guess the simplest question is, do you have an agenda and an exit strategy that leaves your career intact? (And your health...)

Maybe, given the particulars, this is a real opportunity for you. But that's not spelled out at all, nor obviously implied, in your post. And given that this situation was allowed to develop to this extent in the first place, and that you have angry clients to deal with, right off the bat, it doesn't sound promising.

Do you like playing the role of unacknowledged hero who falls on his sword and is cursed by his clueless fellows, while some other protagonist goes on to get the girl?

There is a lot of downside, here. What's the upside? Do the organization's goals and commitments match your personal ones?