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Well, I misread the schematic and got a detail wrong. The oscillator output is not applied to the screen grid…I missed the bypass capacitor which blocks it. The screen grid is connected to the B+ as it should be.
The oscillator output is applied along with the audio to the control grid and likewise the audio is coupled back to the oscillator. This nicely explains the FM you mentioned.
This is not a good way to mix the audio with the RF and my suggestion about plate modulation is worth pursuing. The problem with this circuit is it is depending upon the non linearity of the tube to mix the signals. This generates strong harmonics which not only waste power but cause interference. By letting the tube amplify the RF and the modulation transformer modulate the plate voltage you gain efficiency. The tuned LC circuit in the plate circuit (“the tank”) is very effective in removing the unwanted harmonics provided it is resonant and lightly loaded by the antenna.
The power input (which don’t forget includes the screen grid power) can be controlled by the screen voltage to a certain extent but usually it is best to control it with the RF drive to the control grid as well as the control grid biasing. The more negative the grid with respect to the cathode, the less plate current is drawn. This circuit is biased by the resistor in the cathode and changing this will change the grid bias but it will also be necessary to set the grid drive (oscillator signal into the grid) to the proper level. My guess from the readings on your schematic is that the input power is about 3.7 watts. (cathode current = 7.6V/680 ohms = approximate plate current. This times 332 volts at the plate yields 3.7 watts and doesn’t account for the screen power.)
There is not an unlimited range of screen voltage which is acceptable. If too high, it steals a lot of current from the plate and can overheat, and if too low, it inhibits the electrons on their way to the plate. The tube data sheet might have the recommended screen conditions.
Sorry about my mistake earlier and I hope this information helps.