I have a Dragraces that uses the same principle. The shaft is bent and you can see the score wheels moving up and down. They really have to be lubed well otherwise there is a fair strain on the motor. PDFE (teflon) seems to work well on Dragraces. The bearing is usually a self centring bronze bush.
From memory the second motor/coil drives the shaft backwards to reset wheels but this is on Dragraces, maybe different on this game.
Good luck but has to be done!