Do you have allergies or breed restrictions? I am in a similar boat- and ended up asking breeders of poodles (due to my own allergies) if their breed lines have been used for service animals, what their temperaments are, and the like. Most reputable poodle breeders (and I'd imagine, other breeders as well), keep in contact with their dogs so they know who washed out, etc. Even the dogs that they breed will sometimes become certified therapy dogs, and have certifications for 'canine good citizen' and the like, which points to their ability to train, and ability to meet new people, etc.
I ended up going through the Carolina Poodle Rescue, and they matched me with a dog who will be able to train for 'deep pressure' therapy.
May I also ask, were you doing owner-driven training, or were you working with a trainer who specializes in P-SD?