I believe some States Psychology Board will review transcripts for individuals who are from a non psychology program. So say you completed the MS degree in clinical psychology but for some reason you did not continue with the PsyD/PhD and you worked for a number of years. You then returned to a PsyD program in MFT and completed practicum, predoctoral, and postdoctoral under the supervision of a Psychologist who was a MFT. You can then request for the board to review your training and experience and they may provide you options to gain licensure as a psychologist.
Remember when you were doing your practicum rotations and often there were PsyD MFT or MS level LPC doing practicum placements at the same facility and they were all being supervised by the same supervisors and having group supervision by the same supervisor! A number of States allow Psychologist to supervise MFT and LPC and some are able to include these hours in both their LMFT license application and their Psychologist application.
It was only until about the last 15-20 years that States began having LMFT Boards so now it does not make much sense to try to be licensed as a psychologist if you have MFT training and want to be a MFT. I would think you would go the route of being licensed as a MFT. In the old days, 20 or more years ago, Psychologist were able to do family and marital therapy without further training, but now in many States the MFT Board has restrictions on using the title of family or marital therapist unless you hold licensure under their board. In my State, Psychologist are not able to use the title family or marital therapy but can use relationship therapy.
I question how someone could have already completed the PsyD degree in MFT and not know that most states have MFT licensure and that normally you would not be qualified to become a licensed psychologist. Certainly you were aware of the differences when you went through your PsyD training in MFT?