I don't know anything about Hammond organs but it seems strange that mains is used as a reference frequency unless it has a synchronous blower and uses reeds and pipes. Even then, the pitch is normally determined by the mechanics of the pipes not the exact air flow speed.
I would guess the cheapest simple solution would be a DC PSU and electronic inverter. Mains in --> 12V DC --> Mains out. The advantage being that the mains out frequency is electronically derived.
If it is an electronic organ, the easy solution is to find where it senses 60Hz, which I would expect to be a simple circuit, then replace it with a crystal derived one. It would give frequency stability magnitudes better than a mains derived one.
Brian.