How is your pen set up? If it is in a circle or octagon, it should be secure enough for him to not escape, no? I have 24 and 30 inch pen, one for each bunny. I secure the edges together with metal clips and they stay together. The buns know it's pretty much useless to try to escape. They might try for a bit but given enough time they will realize it's not time well spent. They just run around instead. Toby still tries to chew on the fence every now and again.
Kirby is the same. He comes alive at 11pm. What helped meis changing the time that he eats. I used to give him his dinner salad at 6, no later than 7 and when he finishedthat, then I fed bim pellets,and he would sit and digest/relax until 9 and around 10 he comes out of his cage. By 11 he is ready to play and I am ready to sleep. Now, I put out more hay for him when I come home. I let him eat his pellets around 7, 7:30and gave him salad at 8ish. The combination (I don't know why) seems to make him more likely to come out earlier in the night, maybe it's because I swapped pellet and salad order. Also seems to help: Sitting in the bunny area. He may just come out and investigate why I am sitting in his kingdom.
Another theory I've had since early spring: I make sure I let Kirby see natural sunsetby opening the shades, so he knows it's night time, then the rest of the night I turn on the light... I don't know if he just thinks the days and nights are very short here or what. Basically after dark, the lights turn on from 9pm-1am, then it's dark until sunrise. I have a timer that turns the lamp on and off and adjust it to turn on just after sunset. I have to adjust it every month or so to account for changing day and night length.
It sounds crazy!But seems to help me! Kirby gets up and out much earlier now.