I do know that some iguanas are long-term ravening beasts and can't be safely handled at all. New Kid is not that.
Have you thought about possibly doing the routine of teaching him to be held without fear? It could take quite a while. In a warmed lap. Like heating a blanket in the dryer and putting that in your lap for him to lay on.
When you find is favorite treat, how about offering it to him on the end of a long skewer? That could help him associate you with something good.
Since he doesn't flail, bite, and scratch, I say go for it!
How about putting a tarp on top of the outdoor enclosure, hanging down a couple feet on the sides. That will help him get used to the outdoor environment without having to respond instinctively to the sky. Put large hides in it, so he can hide and chill, getting used to the sounds and smells.
I think New Kid has a great future!