I use the lasagna method (albeit on a much smaller scale than the OP's garden) and it really works. I'm on rock hard clay too. Started with cardboard on top of existing grass and weeds, then layered 18" of peat moss, leaves, straw, manure, etc. Two years later, it's broken down to 6" or so. The best part is how the worms that were drawn to the wet cardboard have broken up the clay and integrated the amendments from the layers- I can now dig much deeper, and it's good black soil all the way down. I've been thinking of adding cover crops to the system, and maybe this will be the year to try it.

That is a great accomplishment.....worms!!

IMO , the qualifier "BEST" does not exist. Method "A" might be BETTER than method "B" but not the best. I much prefer to till and mix everything together rather than layering.
Right now I have layered/buried different stuff in my garden. But come spring I will till and mix everything to have a close to uniform medium. Now I don't think that what I do is the BEST.:twisted: