How to fix cupped drawer bottoms so they'll stay flat
I recently bought a small Eastlake washstand that needs a little TLC. Normally, I try to walk away from fixer-uppers, but it was perfect match for my Eastlake bed and dresser (even down to the wood, which is chestnut), and it just screamed out to me. It was also dirt cheap, so I was willing to take it on.
The most serious problem is that the bottoms of the two narrow drawers are seriously cupped. The drawers are only 9" wide, and the gap between the bottom of the drawer and the back of the drawer is about 3/8" at the widest point, so the cupping is significant. Oddly (to my mind), the top drawer, which spans the full width of the washstand, doesn't have this problem.
What is the best way to fix this? I tried steaming the concave side (the top) of one of the drawer bottoms, and the wood straightened out easily, but the cupping returned when the wood dried. I didn't put any weight on it while it was drying because I was afraid of damaging it and decided I'd better get some expert advice before doing anything else.
Could one of you experts please explain (in detail) how to fix these so that they'll stay fixed? I know they shouldn't be nailed. Assuming that steaming is the way to go, how long should I steam them (just until they straighten out, or a while longer)? Would using weights while they dry help them stay flat? How much weight can I safely use without cracking the wood, and how long should I leave the weight in place?
The drawer bottoms currently have no finish of any kind. (The finish on the exposed wood is shellac.) Would putting a finish on them help keep them from cupping, and if so, what should I use?
P.S. Obviously, I could just replace the drawer bottoms, but I'd only do that as last resort.