It seems that there is a lot that remains to be discovered about the vocal tract and that, in any case, it would be horrendously complicated to try to derive the setup of all the articulators just from the acoustic signal. There are some interesting videos on YT featuring voice / accent coaches, and there's quite a lot of talk in those videos about "oral posture" (for example, one coach suggests finding the oral posture for RP by putting your finger between your teeth).
If oral posture cannot be recovered from the acoustics, how have these people determined it, and how reliable is their information likely to be?