The first step should be to look at how a Super Regen works.
Now the original question. Can it be done with a FET?
You can see the coil on the gate is 1 millihenry. I wound a piece of wire about 24" long on a core (blue) and it was 1.8 millihenry. Putting a pot across the feedback coil would allow adjusting the circuit with a toroid core coil. So the original question, is it doable? The answer would be found by trying it.
This circuit would only require the input tank to be adjustable. The quench circuit could be fix tuned and the feedback could be adjusted with a pot.
The blue coil frequency response is up to 1Mhz.