It's more that my definition of identity just is something like an internally-forward-flowing, indistinguishable-from-the-inside sequence of observer slices and the definition that other people are pushing just...isn't.

Hm. Does "internally-forward-flowing" mean that stateA is a (primary? major? efficient? not sure if there's a technical term, here) cause of stateB, or does it mean only that internally, stateB remembers "being" stateA?

If the former, then I think you and I actually agree.