Hi,
I remember playing around with setups like those for years when i was
into that sort of thing. I didn't like having to mount the tuning cap
on insulators from the chassis so i usually had the principal tuning
to chassis, unlike some of those where the tuner is not grounded.
In those days you could buy fairly small high voltage batteries quite
easily. 67 volt and 90 volt packs were fairly common i think.
I don't remember any battery valves that had more than one amplifier
in the same envelope, although i think that diodes were included with
some battery valves. I used to use frame aerials on the sets i made
in preference to normal aerials, i would wind the frame aerial to be
the tuning coil, and include two other individual windings with it
one for the reaction, and one for the audio pick up to be fed back to
the input, i found that an RF choke worked better than relying on the
speaker transformer to act as an RF choke. I also found that by using
diodes to make the audio (detect) and feed it back to the grid circuit
i got better results than by relying on the valve to self-detect.
There are many circuits like that, they all rely on the RF being
superimposed on the audio from the valves point of view, the valve
amplifies both, so you get extra gain from that stage.
There is another reactive circuit which i have heard of but never tried
where the feedback is much higher, but the circuit is prevented from
oscillating by being 'quenched' at a supersonic rate, this is supposed
to give about the maximum gain achievable from reactive circuits.
I don't remember the name for that circuit.
And i doubt its only one valve.
Best of luck with it, John