Yes you could spread it 6" on top of grass and that should prevent any regrowth, except for any significant patches of couch grass, bindweed etc. Cardboard is not necessary with that thickness of organic matter and I just posted two more pics on the ‘No Dig Vegetables’ banner, of filling a bed with 6" organic matter and no cardboard. That one had wooden sides because it is a stand-alone bed, otherwise I do not use them.
The clods should break up over months when spred on the surface, I would knock them around as well, and they will decompose better in a heap if you can break them up as it sounds rather airless. Definitely cover because it is so wet already, worms will eventually sort it out