I feel KMG and Zig are spot on here.
The most handleable, larger sized animals that fit that cage size are carpets IMO. I'd also say any of the island boa constrictors will fit the bill. Probably a male, but you'll likely get more length with a carpet.
My locality Colombian boa is very arboreal and active, but I'd say he's a bit too large in some ways for the cage size you are looking at.
I had a male SD X Dwarf X mainland retic (not recommended) that was extremely arboreal however he was in a 6' X 2' X 30" cage and was pushing 9 feet. All around he was too ill tempered to manage here.
The most arboreal snake I have here is a male, Bredli python.
I have a female Brisbane coastal in the exact cage size the OP is looking at and she is very arboreal as well. Almost every carpet species is highly arboreal.
Bredli in the 4' X 2' X 2'
He's moved into a 4' X 30" X 20". It has less height but it is deeper. I tend to rotate the adults in and out of the larger cages.
Currently the new Brisbane coastal is in the 4x2x2,
I'm not sure if I will run into any caging issues down the road. Both the Bredli and the Brissy have the potential to get larger. The Bredli is heavy and still growing. The Brissy is very young and may get very long.
My boa is 6+ feet and I don't see him ever going into the 4x2x2. He's too dense and is pretty hard on caging items.
The carpets are more graceful and even at a greater length they tend to be easier to keep in smaller cages. They could eventually weigh the same as the boa but I find it unlikely. My previous carpet that passed was in a 4x2x2 for years and she was over 8 feet. I think she actually preferred the 4x2x2 over the bigger cages.
You can't go wrong with a carpet. They typically handle and interact well, are quite hardy and display well.
Southern coastals and the Bredli are normally the largest species.
Jungles are great, northern coastals are usually smaller and there are many more choices.