I have also been looking at the Panasonic cameras for Canon style Claude opportunities.
My S9 is very bolted down and not getting very far. My G9 II takes the ROM dump service mode key combo (AF-ON + PLAY + POWER ON) but the ROM dump options are like your G81 - they dump meta data and camera settings not a firmware dump from RAM so Claude can't take a look at the unencrypted ROM binary. The S9 doesn't even take the key combo which is odd as G9 II and S9 are same gen.
The other avenue in USB PTP commands to trigger a deeper service mode of some sort, but one of these commands crashed my G9 II so I backed off after that. Might be worth probing on a throwaway camera though.
After the GH1 and GH2 hack I think Panasonic bolted down the hatches! Still hopeful it can be figured out though.