Ed, I think your approach is the most practical one if you don't want to totally devote your life to the project.
I'm pretty sure that it was thousands of years of doing exactly that, that gave us "crops" instead of "wild plants". Until the 1800s and Gregor Mendel, what else was there?
I've read that one of the key techniques is watching a VERY LARGE number of plants for desirable rouges. That way you can extract and multiply a favorable mutation or assortment as soon as it occurs in one plant.