Couple of quick and easy tests for the large transistors.
1. With the power OFF, use your meter to check for continuity between ground, and the metal tab of easch transistor.
There should be none. Any transistor which has continuity with ground, is shorted on.
2. With the power ON, clip a jumper lead to the metal tab of Q7, (which drives the A/C relay). Next touch the other end to the ground braid, whilst listening for the A/C relay to click. Just touch quickly and release.
From your earlier measurements, it seems like Q7 might be OK, but Q8 (which controls the line of death kick back), might be bad, as you suspected.
Also have you checked all of the coils in the game for resistance?
