Doppler effect distortion has been a big thing in the HiFi world for a long time, so I am sure you can search out some relevant information there. Doppler is one of the reasons for multi-way speaker systems or horn loading (which reduces excursion).
Which version of the hifi world, though? The $4000 speaker cable one, or the one where you can actually hear the effects without already being told what they are?
I'm quite happy to accept that the effect is real, just asking the questions that try to get a handle on whether or not it's going to be significant for what we hear. And crucially as guitarists most of what we're doing relies on there being some distortion to sound good, so picking up one part and saying 'this is bad distortion' or even claiming to be able to distinguish the effect of one source of distortion from another is always going to fire up the sceptic in me.
As a last observation, a cursory google of Doppler Distortion seems to suggest that it's there in the maths, measurable with the right kit, but not clearly audible to the ear; it's also the case that a guitar speaker with a lowest frequency in the range of 80Hz and a 12" cone is probably not the most likely place to find or hear it, with smaller speakers (and consequent larger throw) being more affected.