Need some advice

How committed is your wife to driving the car? If she is not very enthusiastic then I would not go to all the trouble of building a car she will seldom drive. I have a local Barracuda Buddy with 3 show quality 1969 Barracudas, all automatics. The green car, that he got in 1972, was recently rebuilt for her. Unfortunately, he got a little carried away and she has not driven it a single time. But she does go to all the shows with him.

If you decide to go automatic:
1964 was the last year for push button shifters and is not worth duplicating. The transmissions are PB specific. I'd probably source a factory 1965 automatic floor shift and adapt from there. Somehow a B&M or other after market shifter does not seem right for this car based on your goals. What about seats? If you have a bench, a floor mount auto is not right either. A 4 speed bench would be ok.
1964 transmissions used a ball and trunnion output. Does your car retain the B&T? A floor mount 3 speed was not available in 64 so you need to figure out what was done there. Rather than "floor" the clutch pedal, it is not difficult to swap in an autonaic pedal assy.

4 speed with 273:
Does your 4 speed have the B&T output?
Is the floor hump configured with the 64-65 round hole? Not a requirement.
The early 273 used the small bellhousing for the little 9-1/4" clutch, weakest item in the whole drivetrain.
Cooling system.
Center link.
Drive shaft.
Shift linkage.
Kickdown linkage.

******

I'm changing over to a 4 speed in my 64 Val convertible retaining the /6 so Im going through this. Original 3-on-the-tree. I don't have a build thread but it has been challenging. Ready to put the engine and trans in early next week. (after Woodward)

Edit: I see Professor Fate is on the same page.