I have had cds turrets move while attached to a pack. M1's never have for me. This is a big consideration for me. Nothing like a guess of zero on a large deer.
I have the Burris' C4 scope, like Leupold's CDS.
I have the scope marked how many revolutions from grounded the zero is. On mine, with my load, two and 1/2 revolutions bring me back to true zero.
I'm sure that's the same with the CDS.
I just print a label with the info and stick it on the objective bell.