Yes indeed, toe-in will undoubtedly have an effect on phantom image position (as explained on the pdf I uploaded). The way I see it, or at least I’ve empirically perceived, about the ratio of reflected vs direct sound, is that it affects the soundstage, how wide, how much depth or how much “3D like” the presentation feels.
My subjective appreciation after testing:
Direct sound: more like “in studio sound”, very focused or pinpoint, and not so big sound stage. Reflected: wider, like a “wall of sound”, bigger sound, livelier.
The thing about phantom image shifting if you are close enough to one of the sepakers is that since you are closer...sound time arrival is earlier than the other speaker, and our brain cares about that, so there isn’t any work around that, it’s the physics of listening to Stereo.