The headphones (K6 and UV8DP), particularly the latter, were causing significant issues. Reducing the volume to a very low level helped somewhat.
The UV88, 88S, 328, and UV5RH models do not have this issue.
It's not broken; it was this way from the factory. I used a similar one from North Star back in the early 2000s, and it was the same.
I previously tried connecting a K6, but didn't see any improvement by adding capacitors in parallel on the speaker.
Are there any other ways to improve this?