Ok, car door's back in...
These are my notes on the FDIM:
According to the car ground, the black and red wires are ~11v & ~20v which gives 9v to power the screen.
The two devices on the left are on the small controller board, see first & third pictures. The one on the right is the large controller board's LF33 3.3v regulator, see last picture. I also measured quite a few of the pins connecting the two boards together. I stopped writing them down when I could see they were all the same, except pin 47 which had an odd mid-range voltage. "Thermal Shutdown" was shown to me on the screen after I took all these measurements, doesn't seem to have been any permanent issues though.