Gumbo,

What is the pH of the subsoil?

Are your Zinc levels OK?

High-clay low-OM soils simply have 'bad attitude.'  No mechanical manipulation will help rooting over the long-term, and sounds like you've tried that anyway.  My suggestions would be to A) make sure you're planting the corn at the proper depth of ~ 2" so that crown roots develop normally, B) make sure the slickened sidewall of the furrow is disrupted by spoked closing wheels (choose your flavor), and C) check the nutrition, perhaps by taking tissue samples of the ear leaves, along with soil tests -- sample both good and poor areas to get some sort of benchmark.  Tissue analyses require some interpretation, so discuss them w/ someone knowledgeable before making any conclusions.

Cover crops have been discussed.  Another possibility to help build soil OM would be to spread manure or poultry litter.

One final thought would be to adjust plant population downward slightly -- excessive crowding adds stress, which may ultimately curtail rooting depth if bad enough.  Hybrid selection can be important, since some have much better ability to handle the clay soils that impede rooting.