In this case the load does not seem to be the problem, but some kind of RF feedback into the reg circuit. ( The Ameriton has it's own supply).
Running a turn or two of the power leads through a "clip-on" ferrite cylinder and a maybe even a .05 ceramic across the terminals should help as already suggested.
That being said, I suspect that that you don't have proper shack grounding either. Each device should have it's own ground ( not in tandem or Daisey-chained!!!) to the master bussbar, then the bussbar is strapped to a nearby earth ground. All of the above should be as short as possible.
You may have a very high SWR on the antenna side ( even if you tuner can tune it) causing the RF kickback.
What kind of antenna are you using?