GREAT find, Ron.
I understand what you're considering in moving from the Fordomatic to a C4. What many people don't realize is that not all Fordomatics are the same.
The air cooled 312 '56 and late (after April?) water cooled 312 '56 Fordomatic and water cooled 312 '57 Fordomatic used ONLY in the station wagons and ONLY in the Thunderbirds is a different transmission unit from the Fordomatic used behind other 312 passenger car applications. [KEEP READING, there is an exception identified below] Saying it another way, the Fordomatic used behind the 292 engine in the '56 and '57 station wagons is not the same transmission used in the 'P' code 312 station wagon.
My understanding is that the '56 and '57 312 station wagon and '56 and '57 312 Thunderbird Fordomatic transmission case has an additional (5th) clutch pack while all the other Fordomatic units only had four.
IF the red I.D. tag is still on the driver's side of the '56 312 station wagon Fordomatic case, the tag number is:
PAW-B (air cooled trans. with aluminum converter) - ALSO police interceptor 312 applications (cars or station wagons)
PAW-E (water cooled trans. with steel converter) - ALSO police interceptor 312 applications (cars or station wagons)
IF someone swapped a '57 312 station wagon Fordomatic station wagon into your wagon in the last 59 years, the tag number would be:
PBA-B (312 with 4 bbl. carb.) - ALSO police interceptor 312 applications (cars and station wagons)
PBA-F (312 with dual quads AND 312 with supercharger) - ALSO police interceptor 312 applications (cars and station wagons)
Another way to identify the Fordomatic transmission cases from the above applications is to look at the left rear face of the trans case, just above the transmission oil pan and to the left of the extension housing and look for a 5/16 (?) hex head steel plug. These cases have the plug, all the other '56 and '57 Fordomatics vehicle applications do not.
Food for thought... Ron, IF you don't use it, you know that someone performance oriented using a Fordomatic would like to have it!
ADDENDUM: I have not listed the transmission I.D. tag numbers for the '56 and '57 Thunderbird Fordomatics that are the same 5 clutch pack units identified above. The reason that the 'Bird I.D. numbers are different is because of the difference in mechanical shift linkage required by the automatic floor shifters used in the 'Birds. The plug on the rear surface of the case mentioned above is the same.
NoShortcuts
a.k.a. Charlie Brown
near Syracuse, New York