You can install the mopar overdrive tranny in these cars with no other modifications other than the cable and electrics. I done the swap in my '50 Plymouth. I think if you find the right car, I'd go for it rather than waiting to find the right car with an overdrive, it might be a longer wait.
You can also install a GM T-5 five speed in these cars, as Don Coatney has done. I'm sure he will chime in here with the details... Don?
Pete