I wouldn't worry about tilling the soil. If you put a new layer of loam down with a bit of fertilizer on top before you lay new sod your grass should still take. Just make sure to water the hell out of it (make sure the roots get SOAKED for a few days after you lay it, or you'll likely get dead spots again.
I have about 6" of loam on top of clay, and have had no problems with my lawn.
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