As John say's in his comment, there is some possibility that the Tung oil is toxic to rabbits.
When we built the 3 story condo below (Dec 2009), we did a a lot of research. Latex was ok in theory, but there was some questions about it.
We ended up going with a soy paint the brand we choose was DuraSoy this was applied over plywood. It has been 4 years now and is holding up well. It was rather pricey as I recall, it has performed well and I would purchase it again. The rabbits have not shown any substantial desire to chew on it.
In this condo, we also use waterproof floor coverings. We purchased some white plastic panels then cut them to size. We cover them with a homemade pillow case (kind of thing), made of heavy cotton fabric. This provides tracktion, waterproof, and is easy to wash.
On the second floor, you can see there is a water bowl, on the dark blue covering. Because the painted surface is rather slippery (in bunny terms) we also put no slip strips on the stairs (there are stairs along the back wall connecting each floor.
The bare wood you see is completely untreated. Sharp edges near the wire are always getting chewed on, so leaving them bare seems to be a good idea.