Chewing is a normally a natural behaviour for rabbits, they chew to obtain food and to investigate and alter their environment. It's not always desirable most people would prefer that their rabbit not chew or dig at cage bars, but it's not "abnormal".
Rabbits are most active at night, just because you'd like to be asleep at 3am doesn't mean that your rabbit wants to be. As far as your rabbit is concerned, by closing the cage door, you have restricted access to parts of his own territory. That's like me putting a lock on some of the rooms in your house and saying you're only allowed in them when I say so. Whilst you may know your rabbit only has to wait patiently for a short time and you'll let them back out, your rabbit doesn't. If he does, he still doesn't understand why you've done it or think it's fair. He's probably frustrated that he's stuck in his cage and he's become bored.
Rabbits are naturally most active in the evenings and early mornings, and sleep most in the afternoon. Your rabbit is most likely to chew the bars when confined at a time he is most active. Try noting when your rabbit sleeps and when he is active and adjusting your routine so he gets exercise during the active period to wear him out. Remember a rabbit should spend a minimum of 4-6 hours per day in an area large enough to exercise in; the smaller the cage the more time your rabbit will require out.
Try to time your routine so that your rabbit exercises and then goes back to his cage for mealtime. This will burn off excess energy before being confined and give your rabbit something to do (eating) instead of chewing the bars. It also helps associate going back to the cage with something good (getting dinner).
Increasing the available space often helps, but preventing boredom and frustration is not just about space, it's also about having something to do. Even in a big pen, a rabbit can get bored if there is nothing to occupy him. Rabbits can quickly become bored of toys if they have the same thing available all the time. You'll need to provide a wide range of toys/activities and rotate what is available every day so that your rabbit always has something different to. You could also make available extra toys over night, and take them away in the morning so they stay novel. Toys rabbits like include a box of paper or hay to dig in, things to pick up and throw, tunnels, and different sized cardboard boxes.
Oh, and I believe that I already answered your question on rabbit stress in another forum thread you started.
