For the first time, I found a published circuit that claims to do something that I have wondered about for a while: a single-tube superheterodyne that not only oscillates and mixes RF to IF, but also implements double regeneration, meaning that both the RF tank and the IF tank are both brought to high-gain, near-oscillatory conditions -- all with one tube. Here's the 1935 article: https://archive.org/details/RadioCraft50Years/Radio%20Craft/Radio-Craft-1935-12/page/n20/mode/1up . It uses a tube with multiple grids, a device whose detailed operation is still a bit murky to me.
If it can be done with one tube, then maybe it can also be done with one transistor as well.
Looking through my LTspice folder of various experiments, I found an old circuit where I was able to make (in LTspice) a 1-transistor oscillator that could sustain oscillation at three separate frequencies simultaneously.
Theoretically, if we alter the coupling between the feedback coils and the tank coils, we might be able to reduce the feedback smoothly and achieve regenerative amplification below the oscillation threshold for the RF and IF tanks, while still maintaining the LO oscillation as required for the self-oscillating mixer action.
Even if that could be made to work, there's still the question of how to stably extract the AF signal from such a beast.
Another interesting starting point might be transistor495's circuit for a one-transistor, single-regenerative superhet, where regeneration of the IF tank is achieved by inductive coupling: https://www.transistor495.com/1TrRadio/1TrRadio.html .
I'm currently doing work with a somewhat more complicated double-regenerative superhet (separate oscillators for RF regeneration, IF regeneration, and LO oscillation), and am pretty happy so far with the achievable gain of this configuration. It would be interesting if the double-regenerative architecture could be reduced to one transistor. Surely it would be a nightmare to debug and probably very difficult to operate, but the idea is strangely fascinating to think about...
The 6F7 looks to be a triode pentode combination, i.e. two separate tubes in one bottle, so more like a two transistor device.
I suspect that a pentagrid converter like a 6BE6 or 6BA7, where one of the grids can act as a plate, might also work .
Some of the GE Compactron tubes introduced at the end of the tube era, had three triodes in one bottle.
Win W5JAG