1955 was the last year Buick used the lighter-duty select-shift manual transmission (has a 5-bolt top cover). The general design goes back to the '30s, and some parts interchange even with other GM transmissions of the era. There are still parts floating around out there on the net if we can identify the broken items.
With the unusual shift mechanism and torque ball output this one would not have been that easy to replace with a different transmission type. Have there been major modifications on the car to make some substitute transmission work?
What has been, can be again. (Bob Wills, 1942)