I guess that the amp in question is a push-pull using a shared cathode bias resistor?
With a shared resistor, at lower signal levels, the tubes effectively bypass the resistor, due to the inverted signals at either grid appearing on the cathode and cancelling out.
Only when the signal level goes high enough for one side to cut off (for some part of the wave) is that effect lost.
I suggest that you re-try the comparison with the amp putting out full power.
Bypass caps on the output tubes cathodes are not like preamp ones. The cap is there not to increase gain but rather to stabilize the cathode and it's NFB affect
That's an interesting viewpoint. Is there any further information on it?
My understanding is that cathode bypass works the same for power and pre-amp tubes.
A point to bear in mind, which often gets overlooked, is that the tube's cathode impedance is in parallel with the cathode resistor, and so should be taken into account when calculating a suitable bypass cap value.