I personally think he’d benefit from a friend. My Digger bunny was like that and he’s a whole different rabbit ever since I got him a girlfriend. :0)

Can you just take the cage away and keep in the exercise pen? If you have an adequate size exercise pen then I don’t think you need a cage at all. It will also be easier to clean than a cage.

Will that help him overcome his shyness? Only time can tell for that.

Also have you had a vet look at him to make sure he is healthy and it’s not a medical issue?

I would also try just the xpen. See how he is in there…

You know, my little bunny is similar (and I’ve had him for about the same amount of time). He’s just very slow to get used to new spaces and it took him almost 2 weeks to comfortably go from his cage to his pen and back without having to think about it for a minute first . Now we’ve started leaving the pen open on one side with rugs covering the hardwoods floors and he has yet to venture more than a step out of the pen  I’m sure he’ll get it eventually, so I just keep giving him opportunities to do it on his own time. I bet your bunny is just a little timid like mine and will get over it in time.

Question: what kind of floors do you have? My guy can’t stand slippery floors at first, but once he gets used to them he’s ok (like his cage floor; at first he freaked out unless it was covered with a blanket, but now he’ll hop all over the bare plastic with no problems). If you have hardwood it would probably help to put rugs down. I guess that’s my only tip! Other than patience, but as a previous bunny owner I’m sure you already have that.

Perhaps the cage is a real security for Napoleon. Still after 3 weeks you’d think he’d get curious. Maybe in the previous home there were other animals or flooring that the rabbit had an adversion too. You could try a little ramp down from the cage door, covered in carpet or natural matting. He might feel more secure to venture out on it’s own then. When he does come out, or you bring him out, maybe give a treat too so he associates it with a good thing.
I have a wriggler too when picking it up. Be sure to scoop a hand behind the butt – I find it stops the wriggling a bit but most importantly, it supports the spine.

Well, in some ways that’s good that he feels secure in his cage. 

Have you tried the lying-on-the-floor-and-ignoring-him thing?  That usually works.  If you’re concentrating on something else, a bun will usually get curious and come up to see what you are up to. RESIST the temptation to reach out and pet him – I know it’s hard.  If you can wait he might even climb up on y9ur back to explore. 

Also hand-feeding his veggies will also help him associate you with something other than grabby-hands.

Is he really in the way when you clean the cage or can you get in and clean around him? If you make the xpen available to him to walk into as you clean, he may inspect your work then get out of your way. If he isn’t growling or boxing you while you do it, he just might be OK with you doing it and feel more secure knowing you aren’t going to grab him. I think he views his cage as his safe place as Wendyzski said. Let him have the xpen option available for several days before giving up on it. Maybe set a toy or comfy blanket or grass mattes in it to entice him out, but not far. It may be he needs to take it really slow to regain trust.

Are you able to take the top off the cage ?  Do you have one of those with a plastic bottom that will come apart?  IF so try taking the top off.   Bunny may be more encouraged to come out while you clean.