* I can pretty easily rmv the ceiling underneath. I'm considering just
cleating some sort of backer behind it, and leaving the existing
(damaged) tread in place. Any thoughts on this?

I had a creaky questionable staircase in my '50s house when I moved in.
I did as you suggest and approached it from the bottom. I used 2 X 4s
and joist hangers (the metal things that are used to hang blind joists)
and screwed it all together with a cordless drill. You can gain a
little upward pressure as you screw the hangers in by slanting the
screw up a little. Mine are carpeted and I have no idea what is under
it, but they are solid and squeak free now.