As a quick test you could temporarily pull one cache chip (making sure it's facing the right way when you put it back, of course) and see if it still reports 256K; if so, it's a fake cache board.

The cache size jumpers just reallocate address bits between the tag and address lines going to the data SRAM. The chipset can't actually read the size you have set from the jumpers, instead, it has to test the cache during POST to see where it wraps around, to determine the size. So if something is flaky that could be causing the misdetection of 256K.

@jakethompson1, thanks for the suggestion.
I pulled out U26 and the POST screen still displays 256K L2, so I guess it's a fake cache board.
No problem; it still performs quite OK, somewhere between my DX266 and P75.
Any suggestions on improving its stability?
Should I disable External Cache in the BIOS?

Progress report:
Removing one of the RAM sticks (the small one) seems to have stabilized the system; it now passes the Doom benchmark and I was able to play Hexen for a few minutes.

I guess the next thing to try is to remove all the fake cache chips and replace them with working ones?
I have a few 71256 SA20TP chips; enough to put together 128KB of L2.
Does installing them like this (on the attached image, bottom right) seem OK?
What about the TAG chip, can I just use another 71256 SA20TP ?

yes that is the correct way to insert them, you probably can use the same IC for the tag if you have enough of them

And ... yes!
It works now.
The POST screen still shows 256KB, of course.
Thanks jakethompson1 for directing my attention to the fake chips and thanks maxtherabbit for letting me know that those spare SRAMs should work.

Br