I had a book called Lasagna Gardening. I used that for a while, it seemed to work well for me.
I put up retaining stones and built the garden up. I don't have that house any more, but I'm pretty sure it was a two brick high wall (you know those large retaining stones).
I'd say it worked best the year I dumped a lot of grass clippings in. Peat moss also works pretty well.
You do want to test your soil for chemical balance.
I wouldn't worry too much about the roots, the stuff you pile on top is supposed to soften the clay, and I had tomato plants going gangbusters. I can't comment on corn because some critter always ate my plants before they'd produce ears.
But basically, build up, add some like composted manure, mushroom compost, peat moss, glass clippings, and good stuff you can get. And maybe some other additives based on your tests.
Good luck and have fun - next year I guess....
Nancy