The only carpeting plants I've ever had any luck with in my low-tech tanks are dwarf sag and clover fern (Marsilea crenata). Both have pros and cons.
Dwarf sag doesn't carpet densely, in my experience, but densely enough to look good in larger tanks. In my tanks, it seems to be fairly short-lived: It goes crazy for a year or so, then gradually dies out over the next couple years.
Marsilea crenata is a great plant. It requires at least medium light to form a carpet, and it takes a couple months to convert to its submerged form, during which time it looks ugly and you'll think it's dying. But once it converts, it will cover the bottom of your tank with small, teardrop shaped leaves. It is quite beautiful and fairly bomb-proof once it gets going.
@jaylach , I wonder if your sag is sending runners above ground because it doesn't like the gravel. In my experience it will send most of its runners just under the surface of the sand. It's possible that it finds the gravel too much work, so does it the easy way.