TKD, rye starts germinating when the ground temp is around 50 degrees, so you may be close or at that temp in SW LA. That would be the first thing I would do. If you've got the ability to water the germinating rye, then your results should be much better.
I've also used construction site silt fencing in problem areas, and it's worked well too. I removed the fences once I got a good stand of grass.
Not sure there's much you can do to permanently clear your water until the erosion is at least controlled.
