I've found that my big girl (around 12-13 feet) likes to 'hide' in the covered part of her cage (she's currently in an 8'L X 2'D X 2'T cage I built out of melamine). She only has windows on the front, and half the cage front has curtains over those doors for a secluded area. She spends about half of her time in the curtained off area, whether under her basking lamp or just past it in a slightly cooler area. I've found that most of my smaller snakes like a bit more seclusion than a glass aquarium offers, or even a cage with multiple clear sides, so that they don't feel so exposed. I see them out more than when I kept them in tanks, so the opaque sides seem to benefit them. I now cover the sides of what tanks I still use so that those snakes get the same sense of privacy (for lack of a better word) that those in my Vision cages or melamine cages get. I figure the same preferences would apply to large snakes as well.
I've never known either my large female or my yearling albino to try to burrow or hide under the substrate - when I used one that could be burrowed under. I use cotton sheets now (easier to clean and still look nice enough). As long as they have a secluded area, either curtained off as with my big cage or a hide for a smaller one, they do just fine. In regards to your cage plans, I wouldn't worry so much about making the cage taller (2 to 2 1/2 feet is plenty tall for adult burms as they don't climb) but I would make it deeper (at least 3 feet). My current cage is only 2 feet deep, and it's a bit cramped for my big girl, but I built it with materials I already had on hand (as my big girl was an unplanned adoption). As money allows, I intend to build a deeper cage (3 feet deep) but hoping to build one 4 feet deep sometime in the future when I have the floor space so I can give her as much room to move around as possible.
Good luck with your cage building! It's pretty rewarding to look at it and know you built it. 
Raven