Hey Randilyn,
I think anyone that's ever owned a burm has run into the same problem. The only type of bowl that I have found to ward off tips are HUGE heavy ceramic ones. But still, during feeding, it's getting sloshed around.
Around 50% of my cages are wooden and of my own design. There's a few ways I've sealed them while building them in the past.
My job gives me access to large pieces of leftover sheet vinyl...same stuff installed in kitchen and bathroom floors. I install it on the floor and flash it about 6" minimum up the sides. All corners and joints are sealed with acrylic caulking. This works great, even for my high humidty species like eyelash and trim trigs. And I've used it in burm cages too. It can be a pain to work with if you're not familiar with it though. Has to be glued down with a notched trowel and rolled out.
Another is melamine tile board. Same deal, but these are rigid sheets. I install them and flash them up the sides the same way, acrylic caulking, etc. Except you can just use beads of liquid nail to adhere it. I have noticed that the melamine finish does begin to crack and chip after time with constant-heavy- dampness though. Considering you probably won't be spraying your burm down daily...shouldn't be a problem.
My latest try is with fiberglass sheeting. And I think this will be my top choice from now on. It costs more when compared to the others, up to around $30/ 8'x4' sheet. But totally water proof and extremely durable. I just finished two new retic cages with it. If you're interested in checking them out, let me know and I'll take some pics. This stuff is so durable that a friend of mine used it to cover the floor of his 75lb water monitor's cage. The cage floor was wooden with a layer of tileboard over top of the ply, and the monitor scratched his way right through it originally. He repaired the floor and sealed it with this fiberglass sheeting and hasn't had another problem since.
Good luck...
Joe @ HellFire Reptiles