Ah the dreaded hum problem...does it do it even with your Les Paul? If so, and ground lifts aren't helping, try checking and making sure your cables are in good shape and of good quality. Also if your amps are on top of each other or too close sometimes that can cause some humming issues due to the amp's transformers being close to each other. How old are your tubes? Have you changed the tubes recently? Maybe try decreasing the amount of gain you are using. Too many players slop on the gain and wonder why the amps hum so bad. Do you have any other amps that you can compare with your guitars to make sure it's the amps? Also, what are you using to split the HRD and Hiwatt? Unless you are using a HIGH quality ABY selector or splitter you will get terrible hum. I use quite a bit of gain, two heads that sit right on top of each other, tons of pedals and cables, and an ABY pedal. My rig is just about silent when I'm not playing. The thing that saved me was a quality power strip that has a power conditioner and my Voodoo Lab Amp Selector. The ground lifts on that baby really do get rid of amp hum and just makes the rig sound cleaner than any other ABY pedal I've ever used. Hope this helps. Best of luck!
-Justin
'67 and '74 Fender Twin Reverbs, '74 Marshall 1987 lead mkII, Metro Superlead 100. Pedals from TC Electronic, Ibanez, Dunlop, BK Butler, Electro-Harmonix, Fulltone, Maestro/Gibson, Loopmaster switching, VoodooLab, Boss. Gibson and Fender guitars, Dimarzio pickups.