Help with piccolo j-310 pincushion

[Alex KL-1]

Bipolar caps comes with categories/types; rarer ones are for high ripple content. These are special ones, sometimes also found in tweeters in intermediate quality coaxial speakers.
If space allows you can use a film cap; heat problem solved.
But about the function of this cap... this serves for the H. linearity at one side; this don't affects pincushion, at least directly.
You mentioned about this cap being connected directly to ground, so I suppose this model not having any pincushion correction (special inductors or dedicated circuit. Some TV's really don't have any; they rely only on the CRT quality/design. And this can varies...
I've seen some pincushioning present on some 5" color CRT, but I cannot assume all need being the same.