What works for us is Abruzzi Cereal Rye on sandy sites in SE Alabama. It works great with throw and mow. Spread seed/fertilizer and then mow. Sandy soil in this scenario allows for the seed to work its way in. Soil will slowly improve each year. I like to go a with a higher seeding rate in sandy spots.
Yep.....it'll really help to stop tilling and build topsoil as well