The treble bleed is certainly not causing the hum - it never did in any guitar I had it in.
So it's the three BL equipped guitars humming through only the ZT and the POD but not through your other amps, and not other guitars through the ZT and POD. And the hum disappears when you touch the strings or the bridge, right?

Very strange - never seen anything like this. Sorry that I am not of much help, really.

Good luck,
Stephan