Final update.

The Pentium MMX 233 isn't working. It crashes with Quake after 20-30 minutes, but the non-MMX chip ran it all night (8+ hours) without crashing.

I'm not sure if the CPU is bad (it was sold "as-is") or not though. I've found a decent price on a Pentium MMX 200 Overdrive chip so I'm going to give that a try. (I mostly want the MMX for setmul capability to slow the CPU for older games)

EDIT: ...and now today it's running for 2+ hours on the Pentium 233 MMX. I'm losing my mind.
EDIT2: OK ... Two hours and it froze again.

It's very possible that the board's chipset doesn't properly support the bus speed you've selected, or has difficulty with it due to age. The power supply being flaky would also cause this.
First step is to always simplify configuration, it could just be one random card causing everything to be unhappy at random points. I'd recommend removing as much as you can to run the benchmark.

Heat is not the only concern with running CPUs over their rated voltage - The actual die can begin to break down under the added stress. Even running ice cold it will reduce their lifetime, sometimes considerably.

FAMICOMASTER wrote on 2021-06-09, 07:56:

Dug her out of storage to see how she was doing, just as poor as I remember it

Thanks for the photo. I find it surprising that, as the inventor of AT form factor, IBM has picked a nonstandard MB design. It's rare to see a 430TX-based MB has a cache-on-a-stick socket next to CPU.

Hi everyone, I just stumbled across this video on my YouTube feed showcasing these custom made VRM PCBs. It looks very promising for anyone that would like to upgrade their socket 7 motherboard with a Pentium MMX:

https://youtu.be/CMiGVQbMC5U?t=980