DerbyDad03 wrote:

I think that they are solid wood (?) because I don't see any plies.
Did they use plywood for drawer bottoms back then?

http://imgur.com/pRNq7Ab

In any case, the insides of the drawers are finished and I don't want
to replace the bottoms. Again, suggestions for flattening them would
be most welcome.

Is this picture of the front of the drawer? If so, it appears to have a
molded edge that extends slightly beyond the front; is that correct? Is the
bottom flush to the bottom of the drawer front; i.e., nor set into a groove?

Is the bottom nailed to the borrom edge of the back?

Groove or on top of a batten? How is it attached to the sides? In either
case, how much do the sides extend below the bottom?