Hi, Kris,
Does it look as if the bracket/flange has broken off the door, or the door has been changed at some time? The flange was spot-welded to the door, AIR. I always thought there was too much strain on the flange and switches when closing the door, and used to move the bracket holding the switches to reduce it.
I think Star Trek Next Gen will work alright with the 'Coin Door open' switch open, and the power cut-out switch can be altered so its two circuits are 'made' with the plunger out. The power cut-out (with six terminals) is actually two entirely separate switches, of three terminals each. One is used for the 50v power and the other for 20v.
Look carefully at the lettering on the switch casing. For each section, there are terminals 'Com'(mon), 'NC' (Normally Closed) and 'NO' (Normally Open). Leave the wire on Com alone, and move the other from NO to NC (or vice-versa). The switch should now be 'made' with the plunger out, and would cut off the circuits if it was pushed in.
If you're lucky, though, it may be a '2-way' switch, where the plunger can be pulled further out of the housing. This puts the contacts back in the same state as when the plunger is pushed right in.