Can we talk about how one 6x6 post took me a whole weekend to pull out of clay
That chunk of concrete at the bottom was the size of a watermelon and I want to know if anybody has a trick that does not involve a shovel, a farm jack, and a lot of swearing.
That concrete blob is the real enemy here, not the post itself. If I were you I'd dig around the top of that chunk a little with a pressure washer or even just a hose on full blast. Water breaks up clay way better than a shovel ever will, and once it's muddy down there you can work the post side to side until it breaks loose from the concrete. Another trick is to drill a few holes into the concrete itself near the post, then soak it. Sometimes it cracks apart on its own after a good freeze. If you've got a buddy with a truck, chain it up low and give it a slow steady pull instead of yanking. Slow wins with clay every time.