Does your vet specialize in reptiles? Or are they a dog/cat vet who will see reptiles?
Vets have to be able to see lots of different animals, but that doesn't always mean that they're well studied in each of those animals.
Also soap comes in many different sizes. Do you have a kitchen scale? Those are perfect for weighing snakes and prey items (although you may not want to put them directly on the scale.)
I recommend trying rats. Your snake might be hesitant at first, due to it being a new type of food, but it'll be easier then feeding him so many mice.