Lumpy lawn and dead patches throughout (Centipede)

After a couple of consecutive wet winters my back lawn looks awful and is now home to many weeds. There’s remnants of dead centipede runners in several large areas that make me look like a lawn care beta.

Ive tried rolling the lumps down with a water roller but my soil contains clay which makes it very tough to flatten. What should I do? Regrade with new soil? Set it on fire?