I would swap the food over for some quality rabbit pellets before starting to add veggies. I recently brought home a bun who was on a terrible diet and that’s what my vet advised me to do. If I am being honest I did it pretty quickly, over just a few days of mixing the old food with the new and cutting the old stuff by half then just completely cut it out. Ron didn’t seem to mind because he actually likes the new food but you might take a bit longer to change over if your bun resists the change. Just mix in some of the new food with a bit of the old and gradually cut down the old and increase the new. I wouldn’t worry about veggies until you have the food change done but you should add veggies slowly only one new veg every few days until your bun is used to it, there is lots of info about what makes a good bunny diet on the house rabbit society website. Good quality hay should make up about 80% of a rabbits diet so you are doing well getting him to eat more of it.

As for the cage what I would do is buy an exercise pen (try typing ‘rabbit playpen’ into amazon and you will see what I mean) and put it around the existing cage leaving the cage door open. It sounds like your bun sees the cage as his safe place but its definitely not big enough if he cant periscope, most shop bought cages aren’t big enough anyway but by keeping it as part of his living space he can still have his safe place but also have enough room. Let him come out on his own. If the cage door opens downwards you can buy a bridge to put over it to make sure he doesn’t catch his feet on it while hopping over it – bramble loved his when he used it but now he doesn’t use his cage at all anymore so has no need for it.

Thank you for taking him in!

That he’s eating hay is so great, that’s the best food for rabbits! Pellets should be switched over gradually by mixing old with new. If he’s a big hay-eater he’s likely to have a good tummy, which makes transitioning easier. Gerbils often get the same food as hamsters and hamsters are not vegan, so the gerbil pellets are probably not right for your bunny. That said, his tummy is used to them, so transitioning is still a good idea.

You can introduce him to veggies, but do it slowly, one veg at a time and only a small piece (like a silver-dollar) for starters. Suitable vegs are romaine lettuce, kale, fresh herbs like mint, parsley, basil, cilantro. Leafy greens are the healthiest for rabbits. Here’s a veggie-list: https://binkybunny.com/BUNNYINFO/VeggieList/tabid/144/Default.aspx

I also second Kirstoyl on the letting him come out on his own-advice. You can sit down on the floor if you like and read or sth, not even look at him (looking at is what predators do before they charge), chances are good his curiosity will get the better of him and he’ll come to explore you. Make sure he has a hidey house (upside down cardboard box with 2 openings in it, one on either side is excellent), so he can withdraw to a safe place when he feels he needs to.

And if you let him have un-supervised playtime outside his cage, make sure you have cable covers on all cables that can’t be placed out of reach! This is important because bunnies have a soft spot for cable-chewing and that can be very hazardous, both for your bunny and for the rest of the family (risk of fire).