The larger the enclosure, the trickier heating often gets. A UTH will not do anything to raise the ambient air temp, unfortunately. If you are going to go with lamps, a ceramic heat emitter will heat the enclosure much more effectively than other bulbs, although it will also zap humidity.
What species of snake are you housing in this enclosure? Are they living there now? I recently had to move one of my snakes into a smaller enclosure temporarily so that I could tinker with the heating in his big boy home. Mine has not yet arrived, but I know radiant heat panels seem to be the heating gold standard. However, with the height of your enclosure, I think you could heat it sufficiently with a lamp on each end. I would ditch the night bulb in favor of a CHE and then keep a basking lamp on a timer at the other end.
That is simply a matter of preference, though. I personally like to give my snakes a day/night cycle and allow for a little evening temperature drop.
You could add some insulation to the sides and top of your enclosure to help it retain heat.
Good luck getting everything adjusted! I know dialing in these things can be a pain, but just think. By the time you get your second snake, you'll be a heating pro. It is inevitable