Or store the last position moved to in FRAM. Fast to write to, nonvolatile like EEPRPOM.
10 trillion write capability. 10,000,000,000,000.
The 28byj-48 are nice & quiet.
Here is one running from a TPIC6B595
Could take a while to acquire 224 of them. I had to order from several sources on Amazon to eventually get 96 of them.
Here are 16 running from a Mega and ULN2003s