An ambitious alternative would be to re-distribute some of that sticky, rocky clay. Use it as a building material or re-grading parts of your yard. . Do you have access to a team of brawny assistants? Or power equipment?
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Use some of it to build walls for raised beds around your yard. Maybe even build up a 12-18" "platform" of clay under a really high raised bed. As long as there is a drainage channel UNDER the downslope part of the new wall, you can fill the center with better soil and have that bed rasied above grade, for a really deep root zone..
2. More ambitiously, chnage the whole grade of your yard for improved drainage, or more water retention. If you have any low spots, move the good topsil aside and fill that low spot with junk clay, then move the good soil back ... now it will above grade and well-drianing.
Maybe create a south-facing slope tio get more sun for one spot.
