Keyboards are quite simple really but hard to explain, I learned by spending hours probing a fullsize board with a multimeter. The dodgy firmware telling you the pins? I came up with that today - no-one's ever had a half known board before and it may never happen again but I do like a problem to solve.
The JSON won't change as that's what letter goes on what key, what you need to change is the pins. I don't do TMK/QMK but if you want to this is what it needs to say, then the GH60 Satan firmware should work:
rows=D0, D1, F6, F7, D5
cols=F0, F1, E6, C7, C6, B7, D4, B1, B0, B5, B4, D7, D6, B3
Or you can use
EasyAVR. Assuming you're in windows download the
windows version extract and run it, that will make a folder C:\Users\your username\.EasyAVR\Boards - save the attached config file in that folder then close and open the program again so it notices it. Then File -> New and chose GH60?? and customise as you want.
Not sure what LEDs you have or if they work? If there are some and they don't let me know and I'll rig something up to find out where they are too.