Check with Olsheln or TSC regarding a KK rake. They make them even for sub CUTs now. The 5' one in the Olsheln catalog is $300. The prices in the catalog are about 10% low compared to local TSC prices for other stuff.
A landscape rake should work for that. You will have to be touchy with the position control so you don’t dig into the grass. Gage wheels help a lot when all you want to do is pick up surface material.