You probably haven't gotten many answers because it's not a common request.
If you created a dual path, and on that second path put an "FX Return Right" block, you could then plug the mix into the "Return/Aux In - Right" port.
From there, the challenge becomes how to hear it. If you move the split path block to the farthest left it will go on the HX Stomp, and hard pan the A and B paths hard right and left, and then at the very end mix the two paths BACK together but again hard pan them right and left, you might be able to plug into the Stomp's "Output - Right" and hear it that way. Some caveats:
1. It might only come in one ear and drive you nuts.
2. This is a complicated cluster of a setup and I could very easily be missing some fine detail that blows it all to hell. My experiments with dual instruments through the Stomp seem to indicate this could work, but I have no way to test it.
Alternate idea:
While you lose the ability to activate the beloved overdrives with one button press (by activating the FX loop), why not just put the overdrives IN FRONT OF the Stomp?
That does a few things for you. One, it frees up yet another one of the Stomp's precious blocks, and two, it frees up the Stomp's FX loop.
With the loop free, it's far easier to do what it is you want. Here it should work if:
1. Split the paths again as before, but this time at the split send all of the signal to Path A with none going to Path B.
2. In Path B place a "Return/Aux In L/Mono" FX block at the start of Path B.
3. Instead of having Path B recombine with path A, send it out of the Stomp's "Send Stereo."
4. In the Stomp's internal global controls, set the headphones to monitor the Stomp's "Send Stereo" port instead of the "Main L/R."
5. Have your sound guy plug the mix into the "Return/Aux In L/Mono."
Doing it this way should allow you to hear the mix as you want to, and you'll have more blocks to play with.