Is there any possibility of moving his habitat to a common area in your house? Living/family rooms are the best. Iguanas observing the everyday activities of their humans get used to it, and it gives them some variability in their surroundings instead of the stark stillness of the bedroom during most of the day. Eventually your guy will be at least a little entertained by it. You will also be able to observe him more closely. IMO this does not violate the No Variations in Routine rule. Rather, the activities become routine to him.
Another, seemingly exotic, but IMO common, problem for (esp. male) iguanas is that from inside their habs, when the interior is more highly illuminated than the surrounding room, is that glass reflects like a see-through mirror, causing him to see his reflection in colorful detail. Some igs assume that it's another iguana invading their territory, and go chronically nuts over it. His best view of himself is when he is on the hab's floor or shelf, looking directly at the glass/Plexiglas. I always advise to cover the first 12 to 18 inches, on the inside, with something that blocks the view. The easiest and cheapest is plain cardboard stuck on with double-sided tape. Anything else he can see himself in, like chrome toaster, spoons, etc. may need to be avoided if you catch him looking intently at it.
Open your blinds when it gets dark, light up the room, and observe this effect. Low-e glass makes it worse.
Have someone make a good hide for you. It looks like an upside-down V. 2 pieces of 1/2 inch plywood, 6 inches x 24 inches, fastened at right angles along the long edges, open at both ends, makes a long enough and stable enough hide. Introduce it two weeks before you move the hab.
I know his cage is a good one, because you mentioned you can go inside it, and because of the vines as part of the decorations. I assume it has shelve(s) and ramps/climbing poles.
This is a widespread iguana-keeper practice: Do you know where he likes to hang out during the day? Try adding a soft piece of carpet there, and a pillow for his head. They love laying on soft objects, and they use the pillow appropriately. Very cute. If he poops on it more than once, that is an act of rejection of the N-n-new! Thing, and in this case it should be removed. But it's worth a try. Make it 16 inches long, 6 inches wide. Glue the pillow to the mattress. He may really like it after several days/weeks.
Any other questions? Hang in there :-)