Add an inch or so of topsoil--instead or proper soil preparation? Not so sure this is a good idea. That much topsoil would be several tons, probably. How many sqft are we talking?
For a thousand sqft--that would be about 3 yards per thousand sqft, or about 3000 to 6000 pounds.
Perhaps it would work better to skip the topsoil and power rake more. Then use double the usual amount of seed. Then water three time per day for 30 days--water is cheap--compared to labor--and you don't want to do this twice.