I’ve been in similar situations, but never without an immediately obvious solution.
That system WILL FAIL. Even as we speak the time-to-failure is shrinking.
Even if one of the solutions described below actually works, you won’t get 100% recovery.
I recall a story years ago - from MIT, if memory serves - where they rebooted a system because they had many generations of Sybase backups. When they tried, it didn’t work. Nobody had actually tested recovering from a backup.
Grit your teeth; cover your ass; and get on with it. The clock IS ticking.