KN2000 corrupting memory at power-on

I've got a strange issue with a KN2000 here.

On power-on, it has some strange memory corruption where it transposes some of the instruments one note up compared to the others (obviously they should all be at the same level) - and the RHS of the keyboard (depending on which sound you choose) has a different transposition to the LHS. Clicking "all initial setting" through the menus cures everything and it stays good for as long as you play - so that's good - but when you turn it off, and then on again, things are corrupted again.

For a little background, I've replaced all the electrolytic capacitors (on all boards) and removed the corrosive glue used to hold the 4x PSU capacitors. I've also replaced the 2x memory backup supercaps. Everything is clean and there was no real corrosion anywhere, except for a little green corrosion on one of the supercap legs (that didn't seem to have affected anything around it, or rather didn't have much around it to touch) but I cleaned and resoldered the area around there to be safe.

The memory issue was present before I opened it (along with some other problems which are now gone, after going over everything), however it hasn't been there the whole time I've owned the keyboard - it was something that began a few years ago.

Now where it gets interesting is, if I turn off the keyboard, drain the supercaps with a resistor, and turn it back on - it says "all initial setting" on boot (as expected), but the strange transposition corruption *still* happens. Again if I go through the menu and reset to initial, all is then well again. Also, if I turn it on and off quickly (monitoring that the supercap voltage stays above 4.5V even when off), the corruption still happens - so this is NOT related to the memory chip losing power.

If it is of use, the supercaps seem to charge to about 4.8V, and then tick down to about 2.3V over the course of 12 hours - I'm not sure if this is an excessively fast drain suggesting that something is drawing more current than it should when off.

I'm suspecting the 256k S-RAM chip and have ordered a replacement - or at least I was suspecting it, until I tried draining the supercaps (so it would be unpowered) and then still having the problem on boot. It seems strange to me that selecting "all initial" through the menus has everything working smoothly (suggesting that the ROM holding the "initial" setting can't be corrupted), but perhaps the way it loads "all initial" at startup is a bit different and the bad S-RAM could still be affecting it? Or perhaps some other bad component that is still affecting it?

All boards are getting correct voltages, and everything works perfectly when the keyboard is powered on (after doing the reset manually) including disk reading, saving and loading, sounds and buttons. This problem only happens when turned on and off.

I think this might be one for the engineer on here, but I appreciate any suggestions.
I'm fairly certain there is a failed IC or SMT component on the board - but how to find which one that is seems difficult. I think the circumstances I've described should narrow it down at least. The extent of my troubleshooting abilities has me suspecting that 256k static RAM chip, hoping to try replacing that tomorrow.

Appreciate any thoughts, and I'll certainly update if I figure it out in case others have similar issues in future.