I have a 40 gal glass aquarium with a screen lid and was having similar problems. I cut two pieces of thick cardboard and wrapped them aluminum foil, then cut out 10 inch holes for my two heat lamps (8.5 inches, one is a ceramic the other is a blue heat bulb), one in each cover. Other than the gap for the heat lamps, the whole lid is covered, but it's loose. It's taped down or anything. That way in the summer I can remove what I don't need. Then I have a moist hide on the warm side (just in case he wants, since my humidity does still drop on occasion) and the cool side I have a small Tupperware (the kind used for sauces and stuff) of water that is zip tied to his branch up near the one of the lamps, and a large water bowl. These alone get my humidity to 38-42% when the tank is covered. Then I have a small hand towel that I soak in hot water and place under the foil but on top of the screen, making sure it does not touch the heat lamps. This keeps my humidity between 48-55%. It goes up to 65% for about an hour or so after I reheat the towel in the morning. Most days I re-wet the towels around 8am and I don't have to get them wet again until the next morning. After 24 hours the side with the small water dish is usually in the low 40's and the side with the large water bowl and moist hide is in the low 50's.

It seems like a lot of work, but once you get a system down it should only take about 3 min. I am in the process of getting a plexi glass lid with holes cut since that would be easier than foil.