Just so there is no confusion. I didn't recommend hay as a fertilizer. You could broadcast legume seeds and they would grow along with ryegrass fixing nitrogen for it. Together they would produce more political promises than either one independently.
You may be too far north for Crimson Clover to be used as a winter annual. Hairy Vetch may be a better choice. I think either would work simply broadcasting seed as you have. Straw is a good mulch and can really help with establishment. The only problem with those two legumes is that they reseed themselves and they would probably hang around a while. But both are recommended for stabilizing weak and disturbed soils.
