Classic/Antique Car Repair: 3 spd manual with o.d., transmission functions, sprag

Question
I have a 57 Chevy with a 3 spd manual w/ overdrive.  When the car is stopped and the O.D. "T" handle is pushed in, the car will not move forward (It will move in reverse). When the car is moving over 45 mph and then the "T" handle is pushed in, the trans will shift into overdrive.  The governor and solenoid work. The solenoid is engaging at 28 mph. When the "T" handle is pulled out, the transmission functions fine as a 3 speed.

Answer
In the over drive unit there is a free wheeling device. It is a sprag or one way clutch device very similar to the over running clutch on a starter drive. Sorry to say that the overdrive will probably have to come out and be overhauled servicing or replacing that one way clutch.
Brad