I live in the St Louis area so my soil is also very clayey.
I make 5 gallons of compost tea each week (from late Spring to earlier Autumn "Fall"Fall") and apply the 5 gallon batch to the front garden one week, then the following week apply a new fresh 5 gallon batch to the back garden. I repeat that cycle for the period given previously.
I have been doing this for 2 years now, and without question I have noticed a massive increase in worm activity eg lots of worm castings on the surface of the soil.
The more worms & good micro organisms you have in your soil, the better your soil will become (at least that is my belief).