I think your vet is right and I think that you have mated at the right time. I have found that vets often differ on the right time but the ones that have more experience in breeding usually say closer to what your vet said.
I had a visiting bitch who was 81 on her first progesterone test. She got the result the next day so it would have been probably quite a bit higher than that when she informed me. She was quite desperate to have pups that cycle and so, with the dog and bitch quite keen, we decided to give it a go with a mating. She had a small litter of 3 pups. I think had it been the day before, when she was 81 she probably would have had a bigger litter. Her cervix can't have been tightly close at a progesterone level of 60.