The more I think about this I doubt it will work as I hoped. I was going to use a coax connector in a T arrangement to hook both antennas to since the power to run the ATAS goes through the coax. While it might drive both motors how would it sense when it was at the correct length for a particular frequency? Normally you have the two sides of a dipole, shall we say a plus and minus as one works with the other. In a screwdriver antenna I just have one side with the vehicle being the counterpoise that it tunes against.
You have to connect one of your screwdrivers to the coax center (as would be the case with
plugging the coax directly to it) and the other has to connect to the coax SHIELD. That makes
it difficult to adjust when the tuning voltage is applied between the coax center and the shield.
The T connector would allow both to tune (assuming that the control circuit would handle
the higher current, which it might not) but would have them in the wrong RF phase. I'm sure
there is a way to separate the RF and DC using capacitors and coils so that the second one
is connected to the center conductor for DC but to ground for RF. (Perhaps you could use
a half wavelength of coax between one antenna and the other to provide a 180 degree phase
shift while still passing DC of the proper polarity.)
To keep the two antennas in sync it would be better to have a single motor driving both
antennas, though I don't know how feasible that is mechanically with the antennas you have.
One approach would be to make two mirror-image antennas with a common tuning shaft,
but that would require a reverse thread on one side to get them to move in unison.