Just cutting a groove and inserting a strip of wood into it would not be much help - the insert would be too thin to do any good. "Breadboard ends" are more like a wide tenon (on the joined panel) going into a wide mortice on a cross-piece of matching thickness. Like this:
Do read the useful
blog entryfor that picture which explains some of the drawbacks of breadboard ends. Even if they do keep your boards flat, they won't look a good fit as a door, especially if your doors are inside the ends of a cabinet (as opposed to being laid onto the ends, like a box lid).
The best approach to solid wood doors is frame and panel construction; it sounds a bit late for that in your case.
However, at only a foot square they are presumably fairly light weight so you might get away with it if your stock is nice and dry and the finished piece is not in an extremely hot/cold place such as a conservatory or kitchen.
One other alternative that might work (depending on the overall piece) is a couple of simple battens horizontally across the insides of the doors.