I would pull the board out of the game for testing, it's easier to access everything and get the meter probes in the right spots.
You were on the right track testing the transistor with your meter in diode test, but here's the exact procedure for testing them:
On the top side of the board, put the black lead of your meter on the metal tab of the transistor you're testing. Keep the black lead there while testing the following:
Put the red lead of your meter on the center lead of a transistor. Your meter should read zero.
Put the red lead of your meter on either outside lead of a transistor one at a time. Your meter should read in the .4 to .6 volt range.
Put the red lead of your meter on the other outside lead of the transistor. Your meter should again read in the .4 to .6 volt range.
If your meter reads anything outside the .4 to .6 range, replace that transistor
Note that this test isn't 100% accurate, as they can sometimes test good even when they're bad. However, if it tests bad with the meter you can pretty much rest assured it's bad. You can always compare readings with other transistors nearby too. If you decide the replace the transistor, it's recommended to use a TIP102 as a substitute for the SE9302 transistors that were originally installed.
Good luck, and share your findings! Ask any questions you run into along the way, too.