There is a possible downside to each of the above options.
The Columbia rear axle is expensive and finding all the correct controls for your year car can get interesting. It is the most correct option for a 39 and will get no points off at judging if done properly. Everything needed is findable, just open your wallet or spend a while searching or both.
The Mitchell is a nice unit. I have ridden in an A with the Mitchell overdrive and Mitchell synchro A transmission and was impressed by both. The downside to the Mitchell is it may not fit under the floor. All the pictures I have seen of a Mitchell under a 33 and later passenger car had the floor under the truck / back seat area cut out and raised to clear the overdrive. I have seen posts where people say they have a Mitchell with no floor cutting needed in a passenger car, but no pictures. If a Mitchell can be installed in a 37-40 passenger car with no floor cutting, I will end up installing at least two in my and my dad's cars.
The F-150 transmission is longer than the stock 3 speed and every picture I have seen of one installed in an early V8 included a cut cross member. Again, I have seen posts that say these transmission can be made to fit with no cutting, but no pictures.