Good idea, but i see there two weak points:
- Rather high losses on the rectifier bridge
- Large and quite highly stressed electrolytic capacitor after the rectifier.

You may try this idea, it address both issues above - it switch directly the AC by ~1kHz (vary with the setting), so no rectifier, nor filtering capacitor is in the power path.
The frequency of the 1kHz was chosen so, it is high enough to not cause visible beat with the mains, but low enough to not cause significant switching losses (with the rather intentionally slow switching - to keep overshoots on the transformer leakage inductance acceptable)...

You are 100% right about the capacitor and the rectifier both get hot after a while I was going to replace the cap cause it's not meant for this load... . Thanks for the circuit.