I gave up on the two transistor circuit and redid it all from scratch using just one transistor on the 12 volt line to reduce the voltage and fed it into the 4069 NOT gate.
To make sure signal voltages input into the bilateral switch were the same, I fed the inverted output back into another NOT gate rather than use the enable line directly.
Anyway, I finished soldering the board. With the 4069 in place, the switching logic feeds into the bilateral are correct. All I have to do now is to solder the RCA's on and try it out, but as it's 11:00 pm here, I thought I'd better call it a day.
I will post some pics and an updated circuit diagram when I get a chance.