I agree. Screened top soil for 4 acres though might be a pricey undertaking.Maybe get some screened topsoil, and spread/top dress the worst areas, then a piece of chainlink fence as a drag harrow to smooth but not destroy the grass? I'd say it's worth the cost of a 6' section of chain link to test if it'll mess the lawn up.
I priced Kentucky 31 grass seed the other day and was shocked to hear $125.00 plus tax per 50 pound bag.
They say 50 pounds of grass seed will cover 10,000 feet. An acre contains 43,560 square feet. So that would indicate 4 and 1 third bags of grass seeds per acre or roughly 2 hundred pounds per acre. So using 2 hundred pounds per acre would cost 500 dollars per acre in grass seeds or 2,000 dollars for grass seed. Then the fertilizer and lime. Dirt is also not cheap per load. Sounds like a expensive project.