The phase inverter is another matter. Because good design demands a
"push-pull" power stage, the output tubes must be fed by phase
inversion of the driver. Good design mandates that the driver has
certain characteristics. The drive should be balanced amplitude wise
and phase wise. The careful phase inversion is the most difficult to
achieve. The Williamson phase inverter was a split load phase
inverter. The plate and cathode resisters of the second section of the
6SN7 were matched at 47 Kohm resisters. This balances the amplitude of
the inverted signal (as long as the load resisters don't drift with
time), but there is a hidden serious flaw, not dealt with by producers
of the Williamson amplifier.

The plate impedance and the cathode impedance are not of the same value
even though the load resisters are the same. This means that at high
frequency, the output of the phase inverter is no longer balanced. A
scope sampling the signal between the two driver signals shows the
discrepancy. This unbalance causes distortion.

Would an easy fix for this be to insert a resistor in the
path between the cathode of the phase splitter and the grid
of the next tube? Once you calculate the impedance of
the cathode, you would subtract that from the value of the
impedance of the plate circuit, and use that number to size the
new resistor. The Rp of the 6SN7 is 7.7K, and with the plate
resistor the plate circuit impedance looks like 6.6K.
The cathode follower impedance =1000000/gm roughly, and
the 6SN7 gets us about 380 ohms. So if I haven't screwed
it up just yet, the new resistor should be 6.2K to
make the impedance look like 6.6K to the grid of one of the
push pull tubes. SO the high frequency rolloff as seen
by both output tubes' grids should look the same, and
thus avoid the above distortions. And thus the global
feedback loop won't have to work so hard.