This might be a place to apply the unbalanced modulator tube idea, using two tubes in parallel for the positive peaks and running high resting current on them, and maybe lower resting current on the negative-side modulator tube, to reduce the DC imbalance in the transformer core. Then drive the two parallel tubes with half of the drive given to the negative tube, and polarize the audio waveform appropriately.
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If you run two tubes in parallel with extra quiescent current, ur more in to class A on that side, with double the current of a single class A tube, and no more positive swing than a class B tube. Actually because ur into class A and the positive side conducts into the negative as well, maybe you'd get more negative peaks than positive?!?
BUT, you could bias one tube in normal class A or AB, and the second tube more like class B, or actually closer to class C, so that as the drive goes up, the second tube "comes to life"... or something like that... there's an audio amp design that used a triode and a screen grid tube together in a similar set up...
_-_-bear