I am not so sure about how sensitive our ears are to discrete changes to timing. Yes, I could hear changes in the sound when I moved my speakers, although certainly not down to fractions of an inch. However, I have mostly considered this more a response to changes in the reverberant field (most of my speakers were dipole or binomial radiators) as I could also perceive change when the angles were changed without any changes in the path distances.
Great additions to the discussion, Bob.
In your example I agree it would be difficult to determine whether the heard differences are timing, room reflections, change in treble dispersion or something else.
Your telephone ringers is a superb example of how we rely on the subtleties of complex sound for our aural understanding of the world.
I feel comfortable that in an acousticly treated studio you would discern minute changes in speaker distance. Consider, for example, stereo recordings made with a pair of omni mics placed a foot apart. There is no appreciable frequency or sound pressure difference between the mic signals. Yet, we will hear a stereo image. This is due to tiny timing differences.
Interestingly, piano is often recorded much, much closer than you describe. Often stereo mics are placed at the "waist" of a grand and then roughly 2/3 of the distance back from they keyboard, both within a couple of inches away. The thinking is that the lows and highs are equally captured. Much closer is also common, placing the mics under the lid and often inches from the strings with the mounts attached to the piano's harp.
Absolutely. Consider the sound stage of a well engineered pop or rock studio recording. The vocals and instruments are often recorded on individual tracks in heavily damped rooms. The perceived soundstage (left to right imaging, room ambiance, depth) is wholly artificial, it never existed in the real world.