The best is to get a 1962 aluminum 727, it will have the parking brake on the back of the trans. This trans will not have park in it. There was no park on th 61 either, and no way to connect it without adding something. The parking brake cable is a different length between 61 and 62 so it would be good to get that cable also.

If you use a 65 727 with a slip yoke you will not have a parking brake on the car at all.

Changing the crank is fine if you would rather work on the engine and leave the trans alone.