A little insight here ...
All of this confusion (and I understand it) regarding swapping trans types among early FORD (1950-60) is the result of lack of info of the exact transmission(s) used and in what exact applications.
The 1955 FORD and BIRD used the BW-259 as direct drive. The OD used was the BW T-86, even though there was a BW-259 OD available. 1957 still used the BW-259, and the BW T-86 OD for FORD and the BW T-85 OD for the BIRD. I do not have a 1956 WSM so that info is not included here, although FORD implemented a lot of updates regarding engine design and transmission usage during that model run.
The 1956 BW T-85 OD must have been introduced later in the 1956 model year. Without more info I have no idea as all of this is not broken down and documented even in FORD PARTS CATALOGING (although it had to be covered in separate service material(s).
I am at a disadvantage as I was more a fan of the MUSCLE CAR ERA and had little interest in pre-1957 FORD. But I understand the frustration(s) many of you have trying to update/strengthen the drive-line.