At the risk of appearing rather negative, there are a LOT of potential problems here.
12 Channel Audio Interface
What is this? A souce of tuning voltage for the varactor diodes?
You need a DC voltage for a varactor, not an audio signal.
What kind of radios?
If they are VHF FM radios, I can see that you would get away with connecting the varactor tuning circuit to the local oscillator in the radio and it would work (sort of).
But if they are AM radios, you are looking at a large capacitance change to tune from station to station, and you will have to also tune the antenna circuit at the same time using a second varactor circuit, otherwise you are likely to be limited to one station you can hear and a few others which you can hardly hear.
The tuning characteristics of the various radios will not be the same, unless they are identical and built in the same batch.
From an electronic point of view, this project would be much easier using modern radios with a synthesiser (as AG suggested).
If you want "old radios", hide the new radios inside the old ones, or just run a pair of wires from the new radio to the speaker in the old radio.
JimB