I agree with you that PSADT has not been validated for very low levels of PSA (below 0.1), but it is validated for PSA over 0.1. I think they like to see at least 3 data points:
/www.mskcc.org/nomograms/prostate/psa-doubling-timeAs for the PET scan, MSK has an ongoing clinical trial of the Ga-68-PSMA-11 PET/MRI that you seem to qualify for:
/clinicaltrials.gov/ct2/show/NCT03204123Call Dr. Wolfgang Weber 212-639-7373 to arrange and find out what the costs are. If the cost for the PSMA PET is too high, and your insurance covers the Axumin scan, he would probably know how to arrange for that at MSK as well.