I like this interesting concept, but if you want to run it open loop like that (without encoders) you can tell if you have any sticking by adding a second limit switch for each motor at the other end of travels. I’m sure you know this.
PC Floppy disks were notorious for running open loop and having only one limit switch and/or mechanical stop at the limit of travel (track 0 sensor). They made a racket if you had more than one, and Much more noise if you had several types, with different track to track settle times.
If only they ran quietly from one end to the other and could TELL you on posting if they were indeed functioning properly.
Your clock would also benefit from more or different switches because if you wanted to Rube Goldberg something to happen electrically, a second pole on the switch could power it, sort of like an indexed relay. Further switches, triggered by the indicator could drive quarterly and half-hour bells, klaxons, fire alarms, air raid sirens, and other fun things. TVBgone everything at a prescribed time?