When I had guinea pigs (approx 3.5 lbs each) THIS was the type of bowls I used screwed down tight to the cage, and put a row of about 8 clothespins around it to keep them from throwing the bowl out of the ring. My ginea pigs seemed to like doing that alot, but the clothespins kept it in place and the pigs had no trouble standing up to the bowl. My cage had a plastic base so I put the bowl on the lowest part of the cage bars I could.

I don't know if rabbits are stronger than guinea pigs or not, or if rabbits will sit up to get in the bowl, but it might be worth a try.

good luck