Ol'55, Here is an article from Hemmings on the BW T-10 that may shed some light on your 4 speed. Also of some help is if you can clean up and post the stamped transmission ID number you can just barely see in the pic below I snagged from your post. Let us know what it is and someone can try and chase down more details.
~ Dan 1951 Chevy 3 window 3100 Follow this story in the DITY Gallery "My Grandpa Carl's Truck and How it Became Mine" 1966 Chevelle (Wife's Hot Rod) | 2013 Chevy Silverado (Current daily driver) US Army MSG Retired (1977-1998) | Com Fac Maint Lead Tech Retired (1998-2021)