Annual rye grass will mostly be gone in one year. With hard and rocky ground like you describe very few of the seed that fall from the plants will even germinate. Annual means it has to come back from seed every year, so you end up with nothing.
For roads and erosion control, plant KY31 Fescue instead. It is the toughest perennial grass you could grow in Virginia. Don't listen to the old fables that it will become invasive and spread everywhere. That doesn't happen. It is aggressive where it is planted, but doesn't start popping up everywhere nearby and taking over everything like they teach in school these days. Some of that ignorant stuff from the so called experts just needs to be ignored.
Best wishes....