The only etiquitte that applies is for your baby, and you, to be comfortable. If he took treats at your new vet, then he is comfortable.
I know this is very, very difficult, but just wanted to say that when the time came for our babies, we asked our vet to visit us at home to help them to the Rainbow Bridge. Everyone is different, and our babies are different, but home was the best option for us when we had to let Bo, then Tess, then Rebel leave us in body. We were able to discuss this with our vet before hand, and he was very happy to visit us at home.
This is such a hard time in anyones life - am thinking of you.