Hi All
Remove the grubscrew from the pulley, use a collar below the pulley to stop it dropping.
Fit a second collar above the pulley with a pivoting lever. Arrange for the lever to drop onto the top surface of the pulley at a shallow angle. When the pulley is driven the end of the lever will dig in and drive the shaft. When the pulley stops the lever will gently trail around the flange.
Improve the drive by cutting a few shallow slots in the flange if needed.
AND/
OR
Get an electronic friend to build a darlington emitter follower to power the motor. Base has 100uF to ground and a preset 47K resistor across the capacitor. To run the motor the timer charges the capacitor to the supply voltage. When the timer times out the voltage to the motor is smoothly reduced to zero at a rate set by the preset.
AND/OR
Add a bit of friction to the disc to slow it more rapidly. Also you could have a solenoid wired across the motor pulling off a brake when the motor was running but stopping the disc quickly when timed out.
If you are making a coin operated machine then a good electronic coin mech would be a very good start. Go to your local coin-op company and shout abuse. They will then throw MS111 obsolete electronic mechs at you. Use enough abuse to also get the front plate mountings and the two orange plastic clips. You can set the mech to accept your wanted coin and reject ( return) all others. Otherwise build an impressive collection of dud coins.
Alan.