I am convinced, that the greatest problem is the stability, which you can not achieve with regen.
When you receive SSB or CW, even some better commercial receivers (such as SONY ICF 7600) are problematic. They do have a simple BFO, and their stability is not superb and the injection locking to strong received signal could be observed.
I recommend you to play with direct conversion receiver, which uses XTAL, Ceramic resonator (7.02MHz was a frequency for satellite) or use some DDS or PLL synthesized LO. Maybe some ultrastable VCO such as VACKAR could be used too, but due to the complexity and a need for isolation it looses the simplicity, which you are (most probably) searching for.
