The 74F74 is an edge-triggered flip-flop. so the correct input for the main 
board is a square wave at TTL voltage levels, with fast rise and fall times, 
but with a current requirement greater than TTL because of the 51 ohm load 
resistor.

As for the oscillation when the doubler is used, the issue may be whether 
there's enough shielding.  The phase detector input of the 74HCT4046 that 
provides signal conditioning is very sensitive...maybe not enough to break into 
oscillation spontaneously, but perhaps enough to sustain it once a feedback 
path has been established with actual RF through the power stage.

73
John