They can do fine in very large tanks - I have a couple that are three and four feet long and three feet high with different levels. However some of them absolutely hate change. My old guy went on a 7 month hunger strike the last time I moved house. He was even in the same vivarium at the end of the process!
I think the initial root cause is the stess of the move. If the vet then diagnosed an infection, it's possible that the stress lowered his immune system and made him more vulnerable.
My first move would be to stop the nightly soaking as this could be adding to the stress and making him even less likely to eat.
As Emily suggested, I'd steer away from misting the entire tank and give him a couple of humid hides instead. I'd agree with the vet that mould growth is a risk if you make his entire environment damp - you don't want to add scale rot to his problems.
Then make sure that he has LOTS of ordinary hides as well. He'll be feeling very insecure and needs to be able to move between warm and cool areas without being seen. Cover the floor with old cereal boxes, kitchen paper tubes, plastic foliage, even crumpled newspaper. Just get anything in there that he can hide under so he can feel safe as he moves around.
Then I'd do the basic husbandry checks. Your temp is 83 desgrees - is that the warm or cool side? The warm side ideally needs to be a few degrees higher, between 85-88 degrees. Make sure you're measuring the temperature at floor level, as that's where he is. Having a thermometer stuck to the side even a couple of inches above the floor, can give a misleading reading.
Then (and I suspect this will be the hardest bit) leave him completely alone for a week. You need to treat him as though he's a new hatchling that you've just bought home, as he gets used to his new environment. No handling, no feeding attempts and minimal checking up on him.
Just a thought as I type though - is there any way you could post a photo so that we could see the flaking skin? It's possible that you could be looking at scale rot already and that needs a different approach (including a very dry environment, newspaper substrate that gets changed daily, wipe the snake with an anti-fungal every other day).