I've had a similar problem connecting my Axe III in 4CM with my JP2C a few months back in my touring rig and this was my experience.
I lifted the ground inside one of the trs ends of a humbuster cable going into the fx loop side and it improved the noise/ screech significantly. Note people say to do this at your own risk, there's plenty of articles online about this approach.
I also purchased the Radial StageBug SB6 that's around $150 to see if that was a better solution.
The results were almost identical to the noise reduction of my modified cable that had a ground lift.
Granted, it's the safer way if you don't want to tamper with your cables, avoid any possible shock, etc.
On top of that, my preset uses noise gate blocks in both the fx loop chain, and in the front chain to eliminate anything else further.
Now here's the kicker, I tried the same 4CM with my Mesa Mark V head with the noise gates bypassed, and my signal was dead silent.
I also have a Mesa Triaxis/2:90 setup that was connected with the same 4CM setup and it was near silent.
Just for fun, had a friend bring over his EVH 5150 Stealth connected to the Axe 4CM and the noise ratio was louder than my JP2C setup.
In conclusion, each amplifier may react differently to a 4CM setup from my personal experience.
Forgot to mention the cable paths. My inputs/outputs reflect my preset routing of how I managed the 4CM.
Guitar to Axe = standard instrument cable
JP input to Axe out1 = humbuster cable
JP fx send to Axe input 3 = ground lifted humbuster cable
JP fx return to Axe out4 = humbuster cable
Hope that helps!