So cable deniers don't believe you need a heavy gauge power cord. I am a "cable denier" of sorts in that I think that 99% if not more of the gain available in a cable can be achieved with an inexpensive but heavy gauge cable.
You have described the exact symptoms of too light a power cable.
I'll tell a quick story. In my tube amp journey I wanted to try a Decware amp. There is a 2 year wait list for decware so I started looking on the preowned market. Being an early riser, I found one listed late saturday night and bought it at 0400 Sunday morning. It was an unpretentious and relatively inexpensive SET. It was only 6 wpc (SE34I.5 for those curious). When the ap arrived there was a note with it "I have included an upgraded power cord I bought for this amp". It was obviously very light. I looked it up, it was only 16 awg and cost $300. This guy had "upgraded" his power cord and ruined the sound from his amp. I was very fortunate to benefit from his misfortune. this amp excells and I eventually upgraded to a top end Decware amp.
As a physicist, I see many examples of google educated scientiists missing the mark and shooting themselves in the foot. Most tube amps are a 200 watt load or less. Look at the book and you'll see that 16 awg is plenty for a 200 watt load. (I think that amp was closer to 100 watts), But dynamics and base require the ability to supply very high currents for very short times. Overall it averages out to 100 to 200 watts, but for short times much higher current is required.
Jerry