I used to manually turn my monitors on/off in this circumstance as well. I was using my Pod X3 Live at the time, and I recall discovering a very strange but coincidentally useful 'feature' of the X3L. This 'feature' (probably unintentional in the design) may prove to have been carried over to the Pod HD500/x devices. If so it will be convenient for you. I have not tested it on the HD500/x, but here goes........
The Amp/Line switch on the top panel of the X3L controls the output level type for the 1/4" outputs. Surprisingly, this switch actually acts as a 1/4" output MUTE switch when it is set in the middle position. Neither the Line or Amp output gets engaged - and so no signal is sent. This only applies to the 1/4" outputs - not the XLR nor (significantly) the headphones. Strange, but true.
So..... IF this behaviour has carried over to the Pod HD500/x devices, and IF you are willing to switch your physical connection from the HD to your monitors from XLR to 1/4", this may be a convenient way for you to achieve what you want: simply use the Line/Amp switch as a mute button.
Worth a try?