I'm not sure the monitor has it's own degaussing coil built in. I noticed a slight improvement in the image yesterday, but still a lot of discoloration. Not sure if it changes when the game is running for some time?
I contacted an "old fashioned" television repairman yesterday (this guy still knows a lot about the old tubes) and he will come over next week or so to check the old tube out.
About the game quitting unexpectedly:
I suspect the power supply too. Sometimes the cab keeps running fine for an hour (yesterday we had great fun with it with the five of us, reaching almost the end of the game, then quitting

) and sometimes it quits on you within 15 minutes. On the moment the machine fails, there is half a second of garbage on the screen (just like when you pull the plug or something) the speakers pop softly and the screen goes dark. All game sounds seize as well, so it's not just the monitor failing and the game continuing, it's the CPU failing.
I checked out the T2 manual and found out that the power supply is putting out +5V (11A) and +12V (2A):

What is the FG connector for?
(found it: Frame Ground) It looks bridged to the +5V line?

Would it be hard to find a new power supply like this one?
Or would it be possible to swap this old PSU out with a different (non-original) one putting out the same voltages? Like a PC power supply (but that will probably not have enough juice for the +5v 11A, I guess)