A motor start cap should be ok. They're meant for intermittent use under
heavy load so they don't accept heavy ripple currents for lomg, but this one
won't have to, with a few tens of kilohms between it and the mains.

A single rectifier in series with 50 ohms feeds the charge current to the
cap. Seems that 150v is a bit overkill, no? (The 25K pot is on the discharge
side of the circuit which is switched in at the appropriate time.)

I think I'm going to go with the 270mfd / 125v start cap. It's sourceable
locally, fits the space, and although a bit low on the capacitance it will
fit the bill better than what's there.