Just for kicks have you tried a different power supply? You stated you first swapped out the power supply upon your first failure and have had trouble ever since. It's probably unlikely but maybe the power supply is not working correctly under load.
1. Swap in a different known good power supply in there
2. I would replace the transistors and mini transistors in question
3. Cut the power wires to the coils that are associated with the blown out transistors.
4. Test coil ohms with wires cut, and diodes on the coils
5. Power up the game with those solenoids removed and see if anything blows.
6. Hopefully everything is still ok at this point, and then reconnect one solenoid coil at a time and power up after each one and test.