Alex, you have correctly spotted Martin Kura's driver as a good code base for adding support for TS0601 _TZE204_dqolcpcp
You can update the driver from here :
https://raw.githubusercontent.com/martinkura-svk/Hubitat/main/Moes%20ZigBee%20Wall%20Switch
In the dev. version 1.0.8, timeStamp 2023/11/20 9:56 AM, the first 6 relays should be supported for on/off switching in the child devices. From the parent device, only the first 4 will be switched on/off.
You will need to delete ("REMOVE DEVICE") and pair the board again to HE.
Can you test and confirm if the first 6 relays are controllable?
Enable the Debug logging, and try to activate relays #7..#12 from the board, if you can do that.
Please copy and paste the debug logs as a text (not as a picture!), enclosed in a summary section (use the forum editor cog wheel tool).
Update: the driver is now available for installation via HPM :