Odd that I do not hear any change at all between no activity and full.
The circuit I use has a 200K pot feeding the plate and screen of a 6BH6, with a fixed 10K resistor to the screen.
Me neither. I never was able to hear RF for some reason.
I guess I was born RF deaf.
I also adjust the screen voltage in my homebrew exciters to adjust the drive level and it does not seem to change the frequency at all, although that has a buffer tube between the vfo and the 6146.
Now you know why it is called a buffer.
I think if you use the generic circuits below you will have a stable oscillator with a buffer that has a variable output for the next stage.
Phil -AC0OB