I think monkey grass would do just fine, and think it's a great idea. Attractive, very thick, small plant, slow spreading. A row of monkey grass is so thick it would act like a check dam.
If it spreads too much, you can give it a sniff of glyphosate wherever your mower won't reach.
I'm currently using bermudagrass for erosion control, and it works OK. Not real pretty to look at, but works.
