If you ever wire a loudspeaker channel the wrong way around, it feels very weird as a lot (but not all for a stereo mix) of the sound will cancel with the other channel in the middle of the speakers and you can move your head through this dead zone.

I've never tried it with headphones, but I suppose even though destructive addition isn't going to happen it might affect things like intended spatial perception.

I understand, and there could very well be some psychoacoustic cancellation when stimulating with a matching tone. But any effect will be regardless of the phase of the signal, because phase cancellation is a physical effect of sound waves that occurs before they are converted to neural activity (where tinnitus originates from).

In simpler terms: tinnitus does not have phase, at least not in the same way a sound wave does.