It's completely normal for the hot side to be quite a bit lower. You are already doing it right with the enclosure type and substrate. Misting isn't something I mess around with aside from just before and during shed, though I do dump a little bit of water on the substrate when it's starting to look too dry and the coco bark sucks it up right away to slowly release it, you just don't want to dump TOO much where its going to stay damp for long. Might take a little bit of experimenting to find the exact right amount and how often.
I have found a room humidifier to help some, but not substantially. I have used a humidifier connected directly to enclosure before for green tree pythons, but never for BP's. You may want to try that on a very low setting (don't want to overdo it with BP) during the winter months where the house heater running zaps a lot of the humidity in the air. Some of the ones specifically meant for reptiles have setting options where you can have it run for specific periods of time rather than all day, which would kind of mimic nature how mornings are a lot more damp rather than consistent throughout the day.
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