63 was a transition year and yes you have the long tail housing transmission which is the same length as the OD. Most 63 through 67 6 cyl trucks had the short housing. You don't need to modify the driveshaft. It looks as though your truck has a floor shift. This could be a problem with the overdrive as there will be interference between the the solenoid, speedometer cable, shift arms, and the shifter itself. It may be easier to locate the column shift components than to find an "overdrive" shifter assembly. You may be able to use the existing one with some modifications and relocation.
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