Well, AFTER I removed the stub of the old round wood fence post, I manage to make about 5 mistakes, even though I hadn't made a single mistake up until then.
The Good: I waited 4 days from last Friday to today, Tuesday, for the water to drain out of the hole, and today I used a sledge hammer to pound the post into the now empty bottom of the hole.
The Bad: I don't know how far to expect to pound it. I eyeballed the post after I took it out, and eyeballed the hole, and said to myself there are one or two inches of water in it, but who really knows. Especially when looking at at the hole from the top of it. To eyeball a tube, you want to see it from the side, not the end.
Mistake 1, I should have taken a steel tape measure and measured from the top of the hole to the water line, then measured the part of the post which was underground when I started pulling it out, then subtracted and figured out how deep the water was.
Mistake 2, Better yet, I should have stuck a dry stick or dry yardstick into the hole and measured how much of it got wet. Simpler and better.
Mistake 3. I should have checked if there were gravel in the bottom of the hole, because even if the water level goes down, I'm not going to be able to pound the post into the gravel. Better yet, I should have put gravel in the hole because I've heard that's a good idea (see replies to other post to find out if it really is.)
Mistake 4. I should have done the pounding on the post BEFORE I filled the rest of the hole with dirt. At least in theory. In reality, I don't think the extra dirt is really making it harder for the post to go down. OTOH, something is, because surely I'm not forcing water out of the hole now, surely it's drained out already, despite the clay and that it didn't drain at all in 2 hours. I've given it 4 days!! And yet the post only moves a little bit with every hit of thI had to pound about 30 times with the sledge to get it to move this far.
Mistake 5. I did note before I started pounding where the post was. I used a couple nails still sticking through the fence section that was leaning against the post, and noted where it was in relatiion to some white flecks on the post. But I should have done a better job, written down the relationship I noted, or something. Because I pounded the post in several short sessions, and I kept being uncertain that I was using the right marks. But I'm pretty certain and I'm up to 1.25 or 1.5 inches already. I'll wait a couple more days and pound some more.
Because the post is still 7' long, and about 2 feet are underground it came up to my nose, so using the sledge was different from normal.