Lawns - Deep layer of roots...thatch? Please help!!

We recently had 4 large oak trees cut down. We had the stumps and all the surrounding above ground roots ground up. Now we are left with a 6-8" layer of fine, dense roots that are spongy feeling when you walk on them. They cover the entire area underneath the canopy area where the trees had been. They are so dense we are having trouble digging them out with a shovel. Is there anything that we can use that would be more helpful, without having to hire someone to come in with big machinery? We would like to level the area and plant sod. Thanks for any advice you can offer.