Does it make sense that because the amp's output impedance starts relatively low on the 8 ohm tap and doesn't have a lot of room to go lower on the other taps, the sound quality would vary less from tap to tap relative to higher output impedance amps, for a given speaker?Yes, with respect to the sonic effects that may result from the interaction of amplifier output impedance with variations of speaker impedance as a function of frequency. And yes, with respect to damping factor. Especially in the case of speakers such as yours where the impedance does not reach low values at any frequency.
However, if a mismatch between the speaker's impedance and the load impedance a particular tap is designed to work into is severe enough there are still likely to be adverse effects on the distortion characteristics and the power capability of the amp. In general, what constitutes "severe enough" is probably hard to predict with any precision.
Best regards,
-- Al