Its like -10mV then stays a little around zero then goes -10mV dances again then up to +10mV in the video, its not steady DC and it is not much DC. So the amp's detector won't react to perceived danger even if it is the same with 100k across the output after probing in the same way.
The dancing doesnt seem to be the problem to me, it should move at least some. The HF must be oscillating and that can be a cap or something feedbacing on the rails
You use SSHV2 I think. Has some JFET thermal drift, the Vref cap is only 10uF to filter it. +/-10mV on 300V does not seem weird to find if it is that.
If there is some excess hiss that would be a problem indeed, not some mV rail dancing