Most of the 55-57 truck 3 speed transmissions I have worked on used a metal driven gear. I think they have 19 teeth. OD's and pass cars used a plastic gear. The metal gear is considerably smaller than the plastic gears. You may be tearing up the plastic gear because it is the wrong application. I have a metal gear I could donate to the cause if it will help.
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