You said that you don't want to take it apart again but you have to ask yourself: Where did the broken teeth go?
They have to be inside the overdrive portion of the transmission, if these broken parts get into the planetary and other moving parts in the OD it will take them out and they get real expensive.
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