OK, got a workaround for this issue in case anyone else has the same problem. It’s not necessarily a mechanical fix but it gets the job done just fine.
The switch on the unit is a momentary single pole double throw (SPDT) and it connects to the player with a little JST / molex connector. It is wired so when the switch is pressed down by the closed door, the connection is shorted and the player boots up as normal. However, because the door on my player is loose, the switch thinks it is open and thus boots into test mode.
My fix was to move the wire on one side of the throw, essentially reversing it. Now when the switch is disengaged, the connection is shorted and the player boots up as normal. If you press the switch, the two wires become open so it boots in the test mode. This works better for my purposes anyway.
I ended up removing the switch from its position on the tray door and set it off to the side. This way, I can boot into test mode by taking the lid off the player and just holding down the switch on start up.
Another fix if your switch is totally broken would just be to jump the two wires, but you’d have to disconnect them to get into test mode.
I made a rough guide with some photos here:
https://imgur.com/a/9PB9956 — hope this helps!