We grow on most of the 'almost an acre' around our home.
A few years ago a neighbor offered to plow up the old garden spot from more than fifty years ago...he used a chisel plow so really loosened deep but I think it was too wet at the time (both to plow and the weight of the tractor) and that added to but did not cause the problem.
We've since only done what is our normal with hand tools, planting cover crops, chop and drop and keep it mulched and planted with mostly annual vegetables although I'm slipping in quite a few perenniels here and there
We only use a broadfork to loosen beds rotating between several beds yearly.
Most is wonderful and loose and grows great crops but there are fist sizes rock hard chunks of clay that are only penetrated by occasional bermuda grass roots. Water slips around the clods just like they were rocks.
Early on I added gypsum and a bit of coarse lime...have not had a soil test.
Patience will win out I know but wondered if anyone has any methods to add?