I never heard of love grass, so I can't comment on it. Centipede is what I've planted along my shoreline, but realize it will take years to establish and do anything. The rest of mine is planted in Bermuda grass. It needs a fair amount of sun, but does OK with some shade.
St. Augastine would work great if there is too much shade for Bermuda, but you have to plant it. No seeds for St. Augastine.
One thing to remember is that you can save a bunch of mony on sod by planting it in a grid pattern and let it grow together. Even a few rows along the dam to stop erosion would give you instant results and fill in over time.
Good luck,
Eddie
