Most of your stuff sounds ok, especially the fact that you're not handling him until he's eating well for you! It sounds like you have a brand new hatchling, based on the size of food and that the breeder said he's only had one shed, is this correct? A 30 gallon tank is way too big for a baby, and can cause them a lot of stress. You could move him into a little tub, section of half the tank so he has a smaller area, or clutter the heck out of the whole tank. And by clutter, I mean at least 4 or 5 hides, fake plants all over, etc. Just stuff it full! This way he won't feel like he's out in the open all the time. You should probably also get some cardboard or construction paper and cover up 3 of the sides (on the outside) so he feels more "contained".

You may also start having troubles regulating the heat and humidity with a screen top tank. You can cover most of the lid with plexiglas or plastic wrap and a towel to help with that. 50-60% humidity should be good, bumping up to 70% while in shed. You do not need to soak a BP to "help" with shed; doing that can actually make the shed worse.

You definitely want to get a thermostat. UTHs can easily cause burns if they are not regulated. You can find one for about $30 on eBay (Hydrofarm brand).

Food size in general should be between 10-15% of the snake's weight. If you don't already have a kitchen scale to weigh your snake, go ahead and get one. It will be invaluable for the rest of your snake's life, as you can use it monitor weight gain or loss, weigh food items, or even use it as intended and measure your own food! Just be sure to clean it first,

I'm still thinking that it wasn't a regurge, especially now that you said it was entirely fur and a tiny piece of bone.