Battery status?

Fixed and working

The battery is working, I mean.

what about leaving just simms or just dips plugged, still giving trouble?

Yes, it needs both to POST at all.

Now that doesnt sound right. It should definitely be able to post with just the DIPs. Maybe has something to do with JP10-15?

I agree, does not sound right.... Those jumpers have Left (simms) and right (dips) "bank o:1". DIPS have bank o and bank 1 printed. SIMMS have banks 0/2 and 1/3 printed.
If jumped left should enable just simms. That era motherboard most likely needs matching 9 chip simms, all my 286 boards do not like the 3 chip types....just some thoughts

I popped the jumpers to the left and removed the RAM chips. It's booting now, reporting 3840kB, which I think is the right amount?
It still locks up though. I only have 1 stick with 9 chips. I assume I need to populate all 4 slots?

afaik 3840kB means its caching bios by default
16 bit cpu = 2 slots at a time

Look at your simms, if two match exactly use just those for now in bank 0, should report about 1792k. See if it stable....you could also loosen the memory timing by adding wait states in BIOS..
You should not mix simm types if at all possible. If filling all banks they should be same type (all 3 chip or all 8 or 9chip) and same speed.

I now popped the jumpers on the other side and removed the RAM chips.
Using sticks with 3 ICs, it counted up to 3840kB, but the system froze sooner or later.
I sourced RAM sticks with 9 ICs, and with those the system is stable.
It still only counts up to 3840kB, no idea where the last 256kB have gone...

bios shadowing + VGA bios shadowing?

Ah yes!
Hmm I wonder what's better on a limited system like this, BIOS + VGA shadowing or the extra 256kB RAM...

Shadowing is better, that 256k will not add much to the 3.84MB (is only 6.7% more). If any app has to get data from one of the BIOS's it will be in ram instead of usually much slower ROM chips.
Glad it works well with the 9-chip simms. Save those 3 chip simms for a 386 motherboard board 😀