It would probably be easier to build this up as one piece and sand it than to make it in two pieces, sand it, and reassemble it. Sanding the underside of the lips is not that difficult. Wrap a sheet of sandpaper around the edge of a piece of 1x 4 or whatever and go at it. If you have a pronounced radius built in, then shape your sandpaper block (rather fast to do with cedar) in the approximate mating shape (round over the edges of the wood block) before you put the sandpaper on it.

Hand sanding such a small area is going to take a few minutes more than sanding with a power tool, but I think you'll save hours over your suggested construction method.

PGJ