an isolation transformer would be a great idea!
yet your power transformer output has one side running through the chassis.
schematic: http://img407.imageshack.us/img407/2723/kay703dw1.jpg
Hot chassis are not fun if you like playing guitar, singing and having lips on your face.
If your wiring in your place are messed up that could cause issues. That would change the hot to neutral on the chassis...
you will inherently get hum out of it from the random grounding points, how much has different factors to do with it.
I personally would rebuild it into a bit different amp, but that is some work and it would be different now wouldn't it :
looks like there is a few different types of 703 by kay.
http://www.schematicheaven.com/bargainbin.htm
I know alot of old fenders used to route one side of the heater through the chassis and you could undo that and fix it..
but since one side of the mains secondary and heater and all signal grounds are going to chassis(most likely) i am not sure where to start!