Hello!
I had a similar problem since I bought my HD500X. Today I managed to solve the problem and finally killed the disturbing hum from the upper-mid range.
I use an Epiphone Les Paul Standard, but I think my solution will work on every guitar (maybe you sould use other Guitar In-Z's described here).
Step 1: Listen to this product test video, type to YT: "Line 6 POD HD All the Amp Models"
Step 2: Find the "Blackface Double Vibrato" AMP at 0:40, your guitar should sound exactly the same as here later! If your sound is distorted you will have to set the pick-up height.
Step 3: Select "Blackface Double Vib" AMP on the board. There should be nothing else in the chain.
Step 4: Go to the "Guitar In-Z" settings, it's at the upper left corner in the software.
Step 5: Switch from "Auto" to "22k".
Step 6: You have to set the pick-up height on your guitar with a screwdriver. Set the pick-ups away from the strings until all the distorsions disapper. If you have more pick-ups you will have to repeat it on each. I tested my sound with a G and D chord because the humming was the strongest by those.
Step 7: Its up to you, but If you use distorsion/overdrive tones more often (as I do) I found that setting the "Guitar In-Z" to "32k" will enhance the distorsion sounds on other AMPS. In the end, I used the same method described here (with Blackface Vib etc.) and set up my guitar to 32k.
Oh 1 more thought: I used 22k and 32k because I couldn't lower my pick-ups anymore at higher Z's to get clean sound.
Good luck and be careful with the settings!