It is always a pleasure to help. I read up on all these things on any case, so may as well discuss it amongst you people.

That hyper-focus on one specific thing, as well as the agitation being displayed whilst repeating the action, may both be the symptoms of AS. They are actually symptoms of AS.
So yes, stimming.

Yes, the rigidity and change causing distsress are both other symptoms of AS. These things are definitely something that can cause agitation.
Ah, now that I think of it! Some of that agitation may likely be caused be things like an unexpected night out to a restaurant, for example. It can be extremely distressing.

So no sudden shift may indicate that it is the AS, though a doctor would be able to say for sure.

Hope this helps!