Your assumptions are wrong about the length of the stock transmission. The "short" transmission was used in 58 in cars and late 62 (up) in trucks. If your transmission has the long tail shaft and has a rear mount it is likely from a Nova or Chevelle from 64/65. It simply replaced the original transmission and you will probably find it will be close to the year of the engine. There is nothing wrong with that transmission with regard to operation, gear ratio, or performance. The original transmission and/or overdrive transmission is 22 1/2 " from the mounting to the end of the tail shaft. If the floor shifter is junk, find the shift linkage components and convert it back. It looks like you are chasing a problem that doesn't exist.
Fred


1956 3100 Pickup/Red/350/3sp OD/PS/Disc Brakes
1957 Bel Air Sport Coupe/Red/355/TH350/PS/Disc Brakes
2017 Silverado LT Single Cab SB/Black/5.3/6 Speed Trans
1947 Willys CJ2A w/F-Head engine