One of the problems I'm struggling with is that I'm trying to recover a signal with a known pattern from under the noise floor and every little bit helps. Varicaps will come into play once there is enough signal that the thermal noise and power supply influence would no longer drown out the signal. Interesting project but it is one of those where when you start you think 'how hard could this be?' only to find out that it is in fact pretty hard. We'll see if I can pull this off or not, I give it 10% chance at the moment.
Oh, and superhet wouldn't work, that would destroy the valuable part of the signal.
What do you mean it would destroy the valuable part of the signal?
If the signal has a carrier (like in AM or FM) or some other regular pattern (e.g. digital signal) then the typical the way to recover it from under the noise floor is to use a narrow-band PLL.
I’m experimenting with it right now and just found that a quartz/ceramic oscillator pulled by a varicap controlled by a PLL gives pretty good results - low phase noise, good noise rejection and ability to recover the carrier from a very noisy signal. But for that to work, the signal has to be shifted to a constant frequency through heterodyning first.