It's been a while since I posted about this set (or on VK in general) so I thought I'd give an update! It was sitting in storage for a while and I finally decided to properly fix it since I know how well these sets perform and it's one of the sets in my collection I like the most.
I replaced all of the white safety caps with the one large four lead cap I soldered to the back of the flyback. It works fine so my math is correct, they do all add up to 0.01uF.
The breaker tripping/shrinking picture problem was indeed the oil cap in the PS as a few here suggested. It was getting untouchably hot before the breaker tripped. Mounted a new 3.5uF motor run cap, problem solved.
I also went ahead and replaced all the small electrolytics on the modules, resoldered some questionable joints and re-tensioned all the connectors and went over the convergence, just general preventative maintenance stuff. And I am pleased to announce it works amazingly well! I think it is one of the best looking color sets in my collection and I am very glad this set finally has a happy ending.
There is ONE more problem I will need to figure out once I procure (or borrow) a high voltage probe. I suspect it is producing excessive HV as even after thoroughly cleaning under the anode cap and the surrounding bell of the tube, it makes a continuous hissing sound and produces a lot of ozone. I've confirmed it's coming from the anode as bringing a screwdriver near it exacerbates the hissing sound, and once or twice I even got an extremely nasty arc that shot out from underneath the cap! The plastic does seem to be decomposing some (getting sticky and oily), so maybe it's becoming conductive? I also noticed the focus control needs to be at its extreme end for the picture to look good, so maybe that also indicates high voltage outside normal operating range? I know focus is often derived from the anode voltage though I am unfamiliar with whether or not that's true with this set specifically - I never did find a schematic for it. I will update if and when I figure that out, but for now the set works well and I am not extremely concerned.