I have a Star, but assume that the carousel motor and gears are the same as your Smart.
If I understood your post, the ball got jammed UNDER the carousel. Never seen this on my machine. All the jams that I have seen on my Star involve jamming between the carousel ball holes and the hopper when two balls try and fit in the same hole. If the jam was UNDER the carousel, this likely put a great deal of stress on the unit and is likely the cause of the broken gears.
My Star occasionally quits feeding balls because the carousel is stopped by a jam and it does not seem to hurt anything, but the jam is not UNDER the carousel. I clear the balls however I can and it always comes back to life. I do not think you can hurt the drive motor and gears by just stopping rotation.
Sounds like you have diagnosed the problem as a hurt gear assembly in the carousel drive assembly. If you are a bit mechanically inclined, it should be easy for you to replace the unit, but you need to make sure the fit upon reassembly is such that the balls cannot get jammed UNDER the carousel.
SP should be very helpful, they always are with me.