For short-term results, you will want to amend your clay with organic material, like
wood chips, and probably some gypsum grit, and yes, till it into the top layers of your soil. No-till is great for maintenance of an established no-till system, but not so good at rapid system establishment.
The organic material is food for bacteria to draw other soil life in, and the gypsum, as well as being a way to add calcium without affecting pH, gives the particles of clay something to stick to besides themselves, making the soil more workable and adding to it's drainage capacity.
If you really wanted to get things kick-started, after the till, treat the whole area with an oxygenated
compost extract and fungal slurries, as detailed in
Dr. Redhawk's List of Epic Soil Threads. They basically put the soil life you want where you want it to turn your clayey dirt and organic matter into living soil.
But let us know how it goes, and good luck.
-CK
A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyze a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects.
-Robert A. Heinlein