Gary,
Attached is the transmission write up from the '57 Buick Product School Manual that details the changes from '56 to '57. It indicates the '57 transmission is a beefed-up version of the '56 unit with different gear ratios. The Buick Master Parts Book shows many of the internal parts are the same from '56-60. Going by that data, the '57-60 units ought to be every bit as reliable as the earlier 6-bolt cover units.
Buick parts books printed around the time these cars were new show the '57-58 models used a case with GM part no 1174880. The '59-60 models show part no 1175493. Later books show the 1174880 for all '57-60 models.
The same cases were used on other GM cars of that era. Oldsmobile's parts book from '62 shows their 3-speed case for '57-62 full-size cars is the 1175493. Yet the '72 book shows the case for '57-64 cars to be a 1174880. The '62 Pontiac parts book shows their '57 model transmission case as a 1175493.
I could not dig up info on the casting numbers. The chances are low that the casting and part numbers are the same. The casting numbers aren't all that useful for identifying parts compared to using the part numbers.
The Buick part numbers for the complete transmission assemblies were different for every year '57-60. The '58 was different from the '57 at the rear yoke of the universal joint. The '58 u-joint yoke was built with missing splines so that the propeller shaft will only stab in one way. See attached page from the '58 Product School Manual. The '57 u-joint would have to be installed to use a later transmission in a '57 car.
I wondered about any differences in the '57-58 transmissions vs. the '59-60 transmissions due to the cable-operated clutch release found on the '57-58 cars. Early on, the Transmission Clutch Gear (input shaft) was a 1174861 in '57-58 and 1189193 in '59-60. Later books show the 1189193 for all four years.
Without comparing every part, the changes in the '59 and '60 transmissions appear to be minor items like internal washers and speedometer drive gears etc.