You have to have a mechanism to separate world as discrete or you have a theory that can't make predictions. If you want to talk about the aligned/anti-aligned beam in the Stern-Gerlach experiment you have to be able to point and say "this represents the world where observers measure aligned, and this bit over here represents the world where observers measure anti-aligned." If you can't do that, you have no theory.

If I understand decoherence well enough (probably I don't), the answer to that is “in you could, yes, but you can't, because thermodynamics”.

This has to be wrong, otherwise MWI would predict violations of Bell inequalities.

I think your 'the world is already split' interpretation is actually the fundamental misunderstanding- I can't make any sense of it other than as a hidden variable theory of the type already experimentally ruled out by Aspect-like experiments.

Edit: Unrelated, but to clarify- you can show that (assuming energy is bounded below) a Lorentz invariant Hamiltonian has a combined CPT symmetry, which can mean a lot of things, depending on dimension. T has to be related to CP, but not necessarily the-same-as, unless you have a state where CP^2 = 1.