When I made mine I used liquid nails along the faces of the wood that were touching along with screws. I also used some kind of caulk on the inside after it was built... maybe redundant sealing but it seems to be working. The box design sounds good but be careful that it will still be balanced. I tried making a box over that lip a while ago and it fit fine but seemed to be kind of top heavy and wobbled around. If you have some type of L-bracket to hold it down it should be fine though. Good luck