[exray]

I can drop the line voltage to about 110VAC with no noticeable loss of performance ... just a little volume. I am tempted to bleed voltage off C to chassis through a resistor to drop the voltage; especially since the set will actually see about 120VAC when plugged into the wall.

I agree with the notion to drop the voltage but that method will increase the load on the transformer. The better method would be to drop the incoming AC using a bucking transformer or even a dropping resistor.

- I can receive local AM, and they sound very good, but the volume fades in and out over the course of about one minute. When out, you can barely hear the station, then it starts coming back and returns to sounding very good.

If its a sudden drop/return bad solder joints are bad for this as are tube cap grid connections as well as the tubes themselves. If its gradual it suggests that a tube grid is floating somehow. Maybe an open grid connection, that type of thing. See above

If I plug the variac directly into the wall, the chassis of the variac is grounded. The
voltage between the variac chassis and radio chassis (again, with 115VAC input) is 56.6VAC

Thats typically the voltage across the line bypass capacitor. Caps do pass AC, ya know! Just like a resistor across a DC source. You won't see it with a low-impedance meter but it will show with a DMM.