The Vision Pro monitor really isn't that old of a device, seems a bit early for needing a full cap kit. The caps in your picture are not damaged, that's just glue used to hold them in place. I don't know if Bob Roberts even carries a kit for this one.
These monitors are *KNOWN* to not work well at all with MCR games.
First I'd try to determine if it really is a problem with the monitor. From the video it's hard to tell, but it looks like the screen is rolling and jumping. If you disconnect the video input and crank up the screen control, can you get a stable grey raster that's not constantly jumping?
You say touching controls on the flyback causes the picture to jump - it shouldn't. Does hitting the side of the cabinet cause the picture to jump too? I think I'd start by pulling the chassis and going over it for cold solder joints, especially around the input header, remote board connection, and the flyback.
Do you have another game you can connect the monitor to?
-Ian