It's interesting this thread came up. I also have an HD500 that I use my L-298TL/L-610 monster with, and I notice the same issue with ground hum; touching the bridge/strings/etc. makes it disappear. I don't believe I've noticed the same on my Micro-equipped Tele and Strat... though both those guitars are significantly more shielded in their cavities (I really should do it on the other one too), and I can't remember whether I have the same problem on my amps (for various reasons I've been using my HD500 almost exclusively lately).

I'll do some further investigation in the next day or two and report my findings.