I plan on making a similar cage at some point and I've put some thought into it. What I plant to do is have a descent looking outer material, like you're wood, but then put plexiglass, acrylic, or glass on the inside. You can get small sheets of it and all the cutting tools in your local big box, reasonably priced. Make a frame of whatever you want, then line the inside, at least the areas likely to be chewed, with the glass. You can glue it in the corners and edges with non-toxic aquarium grade silicone, also found at said store.
One benefit of doing it this way is that you can make it fancier by carving or painting the wood behind the glass, make dividers where they can see each other, etc... There are a lot of possibilities. I'm currently blocked from youtube at work but there is a video you should find readily, where a girl made a play area for her hamsters with white painted plywood on the bottom and three sides. She left the front as just acrylic.
The only thing I'd keep in mind is that you should choose which material you use with the expected wear and tear in mind. Glass easily shatters and can hurt you if you fall into it (I don't think a small animal could break it, even a rabbit). On the other hand, acrylic is more flexible, but easily scratches and may need to be replaced. Doing it this way may be a little more expensive up front, but think of the time and cost of disassembling the entire cage, to replace a chew damaged board.
Lastly, keep ventilation in mind. You don't want your cage to be stuffy and uncomfortable. It can also be unhealthy if fume, like ammonia from pee, hang near the ground. If I was worried about ventilation, I might rig up a place with wire grating like a regular cage and have a pc fan attached to the other side, set to come on periodically and circulate the air. Good luck with it.