Thanks for the suggestions! I took a soil sample by drilling in 5 different spots and combining and the sample is on its way to the extension office. In looking into inexpensive home soil tests, some have cross-checked them with lab tests and found the results to be way off. So my home pH test I have used may also be way off. This "real" soil test result will be nice to have.
Now to till up this heavy clay! What I am doing is lifting the top 8" with a garden digging fork since we just had a little rain to at least soften it up a bit. Then I will cultivate with a tiller. Just a tiller alone won't hardly touch this clay. A large tractor would work but I don't have one and don't want to bother a neighbor to come in, and also it would tear up the other plot I already have. I think the tiller will work fine the way I am doing it.