There are a number of rigs that measure cathode current rather than plate
current. Depending upon the tube, screen current is only a small percentage
of plate current, so even a 10% change in screen current may result in only
in a 1 or 2% in cathode current.

I have one other bizarre thought - which I admit has not been given much
thought - suppose you fed the screen with a constant current source, so that
screen current would not change at resonance?

Also, off this subject and back to screen modulation techniques, the old
Radio Handbook mentions that many beam power tubes will self modulate, with
no additional screen audio supplied. Apparently, it can vary from tube to
tube. Despite that stateement, I know of many am transmitters using beam
plate final tubes that do have audio applied to the screen, so take the
statement with a grain of salt.

73, Colin K7FM