A second variable in the audibility of absolute phase is the speaker design. Audibility is proportional to the degree to which the speaker is phase coherent. For example, if/when one driver's polarity is inverted relative to another driver, absolute phase is less audible vs. a speaker having all drivers in phase (all other things being equal, never the case of course).
Some costly non-polarized caps are marked for output (+) in-circuit, sounding better in this orientation vs. the other. I've auditioned high quality unmarked caps and marked them, then retested the same cap blind and was satisfied to consistently prefer the same orientation.
If above is an accurate indicator, one may surmise that a phase-coherent speaker with properly oriented capacitors may provide maximum audibility of absolute phase.
I certainly applaud Dan for the phase feature, and loved the preamp when it arrived at 2008 T.H.E. Show Las Vegas. The feature is one of the advantages provided by a transformer output coupled tube preamp. Inverting line-level phase requires an extra gain stage unless it is performed by a transformer or a balanced output coupled to a single-ended input (e.g. select pin 2 or pin 3 of XLR balanced output for single-ended phono plug input). An additional gain stage distorts the audibility of absolute phase tests.
I don't know how "clean" is a phase switch in the digital domain.