How do you know its still not a stuck switch causing the coil to repeatedly fire? What was the root cause of your switch matrix issues? "Moving the wires around" caused the coil issues - so you need to revisit what you did to "fix" the switch matrix and verify it isn't the source of your current problems.

Which wire are you disconnecting from the popper? Do the other high power coils have power and work when you disconnect the sniper tower?

The connector is probably not the issue.

If you are changing the TIP36C, the TIP 102 and the 2N5401 each time and the coil is still locking on then the issue is further upstream in the 74LS374.

What is weird is the behavior you describe with the coil connected, namely all of the other activity of the other high power coils. Which is why I was asking about the switches, because many of the switches related to those devices that all power on are in the same column.