Back in the 50s and 60s when the interstate highway system was being built in Texas, my father sold bermuda grass sod for the ROW. They basically cut/scraped the first 6" of soil and hauled it out in dump trucks to spread on the highway. It wasn't the organized operation like it is today. We were left with thin sandy soil.
My dad bought some button clover hay to feed to our cows and spread it around the property. Some of the clover sprouted and took hold, but since nothing more than that was done, it really didn't ever recover. When I sold the property in 1998, it was just beginning to recover, but nothing like it had been before the sod removal. I just can't imagine hay doing that much to regenerate the topsoil. I think Taylortractornut has a much better plan. An agricultural Extension office in your area might also have some good advice.