The distortion is gone completely if I remove the A590. Even if I have the psu turned on near the monitor.
Well, I got the standard Commodore A501 memory upgrade (of which I recently replaced the battery)
It is my belief that the Commodore sidecars were not as tolerant and robust as the GVPs and Supras. I never found an A590, but, I have used several A570s. They don't like anything playing with the CPU timing. The A590 may be as intolerant. Your A501 should not be an issue at all.
Off the cuff, here are some things to try:
Make certain the ground and shield connections between the A500 and A590 are tight and shiny where everything slides together. The grounds of the A500 and A590 should be the same (no voltage between them)!
Consider re-installing the fingered shield bracket that is screwed across the top of the edge connector, if it has been removed.
With everything powered, carefully check the power rails of the A500 and A590. DVMs are inexpensive today.
Power all PSUs from the same power strip (per Amiwest)
Consider an older beefier PC PSU and make new cables to it with Mec's square Amiga connectors. I did this.