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Another option, probably the worst, is to simply replace the pot with two fixed resistors and have a permanently "set" static convergence control.
It would appear that the static convergence control compensates for three dominant sources of error: manufacturing tolerance on the 15GP22 and other parts, which is static and fixed, B+ and B++ boost voltage drift due to line voltage drift, which is variable but can be fixed with a Variac or Sola, and drift in the fixed resistors that make up the divider from the HV rail to ground due to the temp coefficients of the resistors and simple aging, which can be minimized but not elimated.
I'm sure there are other minor sources at play, but those would be the three largest if my crude LTSpice mockup means anything.
Nailing down two out of three, minimizing the third, and using fixed resistors *should* work.
The 15 inch sets at the museum don't seem to need all that frequent adjustment of the static convergence control, and they are of course run straight off mains, with no regulation of the line voltage.
Something to consider if other options don't pan out. You should always run a vintage color set on a Sola or at least a Variac anyway just to avoid stressing components due to today's much higher line voltages, as the utilities desperately try to squeeze every last bit of capacity out of a broken and aging infrastructure.
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