Hmm, according to the manual you need 4 x 128Kx8. Keeping with Winbond brand of CMOS static ram that would be W241024A or equal. Or maybe go with ISSI brand and get IS61C1024-15N.
The manual does not state if the TAG needs be upgraded for but would assume it not since you have a 128byte TAG but am probably wrong. The w24128AK is 16k x 8, wondering if a 32k x 8 24pin might be needed (like W24257AK-15).
Maybe someone else has better info....

No, you need different tag chip too.
You currently have a 16K x 8 but you need a 32K x 8.
It seems your FSB is 33 MHz. Which L2 cache timing do you currently use?

In this board I use 256 K L2 cache in 2 banks with 40 MHz and 2-1-1-1 timing.
I did not succeed with this timing at 40 MHz when having L2 cache in a single bank.

The board will work quite happily with 512K, but you won't get any extra performance out of it. There were a bunch of us who did this about 10 years ago and the consensus was that the amount of cacheable RAM increased (so something like Windows/Linux performance would be improved), but you won't see any games benefit unless those games are using a colossal amount of ram, ie over and above the region cached by 256K.

I indeed operate the FSB on 33 MHz and the timing is 2-1-1-1. I will try to find the chips you advised.