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It can be stressful for them to move cages & I can understand your concern as Arnold has had such an unsettled time before coming home with you but it is important that he has his wheel in the cage, he will mostly be using it at night when you sleep so playpen time isn't enough really.
You can make cage changes minimally stressful by keeping everything, layout etc as familiar as possible, using all the substrate from the old cage, not doing any cleaning except spot cleaning for a couple of weeks before the move so everything has his scent on it & not for at least a few weeks after the move.
It sounds as though he's taken the move to his new home pretty well so he may not be overly stressed by a new cage, it can take any ham a couple of weeks to settle after a change.
What size cage do you have now?

Does he bite out of the cage or just in the cage? If it's just in the cage then he may be a bit territorial which would be understandable given his history, now he has his own space he may not like it being invaded too much!
Try to get him more used to hands during out of cage time, go slow, just begin with letting him come to your hands & explore them, he will probably climb onto your hands soon enough, once he's been doing that for a while you can begin to try handling him a little more, take time over each step forward & don't be tempted to move on too soon & he should gain confidence & be more comfortable with handling.