29″ may not be high enough. Once a bunny decides to jump, and likes to, he may be able to clear that. That’s why most xpens we use are about 36-42″ high. I also think he may attempt to launch off the castle in the center over the side – and could possibly succeed or get hurt in the process.
A suggestion: get a plastic top that is used to cover xpens and attach it around the circumference so he has a cover. You could use a sheet, but it’s a matter of not having holes he can squeeze through above him. But a cover held with clamps might be enough of a deterrent.
You could also invest in a taller xpen, abandon the baby siding and swap it out for the xpen, and build up another layer of cubes to match.
I find that my xpen that is 4’x5′ gives her plenty of room daily to hang out in, so one by itself may be enough, then have the door open to a larger space when you’re home.
Please don’t trust the dog to stay out of the room when you’re gone. But sure to secure the dog as well as the room bunny is in. It only takes one time to be bad for the bunny. They need to be supervised and never alone together, which it sounds like you are trying to do for them.