You have the collector connection to the transistor cut off (middle leg) which is what is needed to be done here. But with the collector pin cut, the only means of connecting the collector is through the tab. But you used an electrical insulating thermal gasket there (thermal gasket is OK) and you also used a nylon screw which is not OK. You must use a metal screw there with a star lock washer on bottom of board so the transistor can make good electrical connection with the trace on the bottom of the board.

TO-66 transistors (old 2N3584) relies on the case to make the input connection. You get the same connection through the tab of the new BUX85.

You *could* isolate the tab from the heatsink but still must make good connection to the trace that shares the same screw hole. To do this, you need to reduce the screw size to a #4 and use something like a 7721-7PPSG nylon shoulder washer. This would be an ideal condition as the heatsink would no longer be connected to high voltage (original design had the heatsink connected to high voltage) but still make connection to the PC board.

See this thread:
https://pinside.com/pinball/forum/topic/replacing-obsolete-ballystern-hv-to-66-transistor-with-more-available-to-220#post-2948736

Not likely. Hot R51 is due to Q23 being fully turned on. Missing collector connection to Q22 (plastic screw) would result in Q23 being fully turned off and R51 would remain cool.
Sounds like Q23 is shorted. Q22 probably isn't too healthy either.

If you replaced Q22 and 23 and they blew in a few minutes, you may have gotten some bad(counterfeit)transistors. Where did you get "kit"?

Anytime i see a burnt / over heating R51 pretty much know the HV section transistors are shorted. Pretty good tell you can pick up at a glance.

too bad 2n3440 goes EBC otherwise it would be safer / easier to use soemthing like MJE3439 or TIP50. Put one of those small TO-220 heat sinks on Q23 but it would be flapping around. I guess you could drill a hole or do some kind of fold over mounting to the right.

Maybe Q22/Q23 failed because because the bux85 collector was floating? Not sure....

It's always best to replace all 3 of those transistors at once. Otherwise you may chase your tail but eventually the merry go-round will stop, and it will work fine. I don't like revisiting problematic high voltage sections, so out with the bad and in with Great Plains good stuff. New filter cap, pot and whatever else looks or measures tired.