If touching the RCA jacks influences the hum, you will want to carefully inspect the grounding inside the amplifier. The most important would be the bare wire connecting the "E" terminal on the IEC jack, the #8 lug, and the grounding terminal on the adjacent 6 lug strip.
If all this is well connected, check the resistance between the #8 screw and terminal 3.
Did you, by chance, paint the bottom of the chassis plate?
I feel pretty confident that there's a loose black wire in your amp, it just may take you a little time to find it.
-PB