First off, you can never let an iguana "win". If you back down from his bad behavior, you are doing exactly what he wants you to do and reinforcing the behavior.
Other first off - get rid of the wire cage! Alright, keep the cage, but make the walls solid. Plexiglas (lexan is cheaper) works. Kinda pricy, but maybe you can do a wall at a time if the cost is an issue. Home Depot sells the Lexan stuff.
The back and even side walls can be plywood. Iguanas do like a view, but ya gotta do what ya gotta do.
A solid walled cage will also hold in the heat better. Top for sure ought to be solid a that's where the heat is going.
As to dealing with getting him out of the cage or getting in there to feed and clean. How about covering him with a towel until you get him retrained. Also cover him with a towel to remove him from the cage. You can get a towel over him and he can't see to attack and you can wrap it around him as you pick him up which will limit his fighting / clawing ability.
Maybe you need to cover his cage for awhile to keep him from charging at it.
When I first got my male rescue (maybe just over 3 feet back then) he would throw a hissy fit when I picked him up. Hoping that I would leave him alone I guess. See sentence 2 above - NEVER let an iguana win.
I would pick him up and he would do his thrashing thing with alligator rolls thrown in for good measure. My method of ending that was to hold him at arm's length as high as I could. That worked in a quickness for settling him down.
Within 2 maybe 3 days there were no more tantrums when I picked him up.
What works for one may not work for all, but maybe it's worth a try.
Give him a bath EVERY day. Same time every day.
If nothing else, he should poop in there thus keeping his cage cleaner. And, he may use up some of the pent up energy "swimming" in the tub.
Have you tried allowing him out to roam around?
Iguanas like a routine. He may not like you so much right now, but I think that they can be trained or at least acclimated to you and what's going on around them. Try your best to do the same thing at the same time each day.
Iguanas aren't like dog smart, but I do think that with some consistency on your part and a bunch of "I can do this" attitude you can turn him around.
Some folks here have had iguanas with territorial and aggression issues that never went away. You may get a story or two from them, no telling.
Might be I got lucky, but I wouldn't throw in the towel in your case if he was well behaved in the past.
What are the temperature ranges in his cage?
How large is it?
Each iguana is different, but I would try a full court press on this guy (no sissying out!) for quite awhile. I would be in his face as often as I could and not back down.
One of you will win. Good luck!