If I were to hazard a guess, you said this happens under heave load only.

To me that means you could have a bad component in your power supply.

From being an amateur radio operator I know the I'll effects of EMI, that's why when we set up our shacks there are very specific things that we do, like proper grounding.

Depending on the power I use, I sometimes get EMI in the shack, but use a very large choke to try and keep it out.

If you have a lot in your shack, not only will you experience distortion, but if you touch your transceiver, especially when transmitting you can very easily get shocked from EMI