Yep, I've tried "no-till gardening", and I've gone back to using a Troy-Built rototiller also. 

Last year I put in 3 raised beds, adding 2 more this year.  My raised beds are small enough that a roto-tiller is not a viable option.

I think the real key is to use compost/ mulch of some kind.  I collect tree leaves (mainly Maple) in the fall, store them, and use them in my garden.  So, I like to incorporate them some, although I also use them as mulch in the summer time. I would think that with a clay soil, as you say, that getting mulch incorporated quickly into the soil will be key.  And of course, using mulch in the growing season to conserve moisture.

I have a small yard, and an even smaller garden. A couple of years back, I decided to move my garden to another spot in my yard.  A lot of the reason for moving the garden was a Maple tree that I planted, and is growing larger and larger. I moved the garden to get it further away from the Maple tree. Well, I planted that area back to grass.  And for the last several years, that grass is much darker green than the rest of my lawn.  I attribute it to the ample (excessive?) amount of leaves/compost which I have incorporated into the soil in that area.