What, whether it is AM or FM or what proportion of which?

Sources don't matter, all that matter is a clean enough signal to analyze.

Point... My memory of modulation theory is that the only difference between AM
and weak FM is the phase of the sidebands. (This is how modern high-powered AM
transmitters are built -- the carrier is weakly FM modulated, then amplified,
then goes through a phase shifter. Or something like that.)

So... If you analyze the sideband frequencies into their AM (in-phase) and FM
(quadrature) components, you have the relative amounts of IM and Doppler
distortion.

The FM component is, by definition, Doppler distortion. (Right? ???) So its
source or cause doesn't matter.