Right, but not that's the same thing I'm wondering about. I'm wondering if the change in mass distribution due to ice migration might set things out of balance

Right, but not that's the same thing I'm wondering about. I'm wondering if the change in mass distribution due to ice migration might set things out of balance such that movement is possible. Further, that could still happen with effective tidal lock. Perhaps it's a "punctuated equilibrium" kind of thing where it's stable for a relatively long period until enough ice builds on the dark side that the planet "rolls" and stays in that position until enough ice melts and migrates again.