You now know the source of the noise. Now you just need to figure out how it's getting into your audio signal.
Do you have any audio cables running close to the RJM? Are your MIDI cables running close to any audio cables or pedals? Separate anything MIDI from anything audio as much as you physically can. If your MIDI cables are shielded, then take a look at the shielding on your audio cables. If you have effects pedals near the RJM, try moving those around. Go through your entire signal chain one component at a time and try to determine where the noise is getting in. You'll likely find some device or cable at which the noise is missing or quiet before but audible or loud after. Sometimes all it takes is physically moving things around a bit to get rid of the interference. If you've got cables or pedals on one side of the RJM, try them on the other side.
You can use the Axe FX to help too. Is the noise louder with high gain patches. If so, then it is likely getting in somewhere before the amp and/or drive blocks. If you are using an FX loop setup, mute those blocks and see if the noise stops. IF so, you know the noise is getting in somewhere in the loop. Does the noise get louder if you turn the output knob up on the Axe FX. IF so, the noise is being amplified by the Axe and is getting into it somewhere. If not, then it might be getting into the cables between the Axe FX and your monitors or power amp. Divide and conquer.