1964 trans problem

The first thing I would do is make sure the shift linkage is working properly with no slop or missing bushings.

Then you probably have a valve body problem. Could be as simple as a sticking valve, but then again the VB could be worn out. Passages and valves do wear. At this point I'd drop the pan and remove the valve body, then thoroughly clean it or take it to a trans shop and have them do it. It's not hard once it's out. I'd get a shop manual first though.

Do you mean that the shift lever goes all the way to park before it tries to go into reverse. That does seem strange. Does first gear work OK? I think it shares the servo with reverse. I took one apart where the servo 'hat' had actually flipped over sideways. Servo adjustment as I recall with the pan off is 1/4" spacer and tighten to 9 in. lbs., then tighten the lock nut. The other one outside upper right is 9 ft. lbs., loosen 3/4 turn and tighten lock nut. The valve body has lots of pieces in it so be prepared with a clean table to lay everything out and a diagram to guide you in getting it back together.   

The TSM has some diagnostic tips in the transmission section.. I think that problem is mentioned. Joe

Ok, I was mistaken about your particular problem being mentioned but it does mention locking up in reverse gear.   It sounds to me like you have a problem with the linkage adjustment.  Further, I think if you drop the pan you can actually see the parking pawl engage when you put it in park (of course the motor can't be running with the pan off).  I think there is a detent ball (or balls) in the shifting mechanism inside the tranny and you need to make sure it (or they) are in place and dropping into the pockets so that you can feel the shifter go into each gear position.