I mean that if you decompose along a different basis than experiencing x/experiencing y, you just get an ensemble of states each of which is a superposition of experiencing x and experiencing y. So you end up with the same thing.

It's like looking at an entangled state (because that's exactly what it is) - if we have a two-particle state like 1/sqrt(2)(|x>|x> + |y>|y>), that behaves like the first particle being in |x> and experiencing the other particle being in |x>, or being in |y> and experiencing the other particle being in |y>, and it might look like that's an artifact of this particular basis decomposition, but it actually isn't - the structure of the wavefunction is that it divides cleanly into those two branches, and that's true in any basis.

> You can't just retreat into "well this is the only basis I can experience" because the human sensory apparatus would be able to select out a range of bases in a full unitary account

A system that's freely interacting will become entangled; whatever we consider ourself is constantly interacting with the rest of ourself, almost by definition.

> also the ambiguity of basis decomposition means you can't perform conditioning which we do all the time in experiments.

Of course you can, and it works exactly the way you'd expect - we already do experiments where some isolated apparatus inside the experiment does something if it detects one thing and something else if it detects something else. Choice of basis is a tool for understanding the wavefunction, not a physically real thing.