When I was a kid I had blackheads along with acne. When I see posts set with concrete like yours have I remember the blackheads and my mom catching me and working them out.
Just like she would pop the blackheads out by putting pressure on the sides of the blackheads your soil is trying to pop the posts out of the ground. When the concrete has a ledge above grade then the ground has something to grab for pushing up and out.
Your expansive soil, the clay, shrinks as it dries out. It pulls away from your concrete footer, the cement around your post. Then when it gets wet it expands, bottom up. This action lifts your posts and pushes them toward the side with the least resistance, you get lean.
Add to this the expansion and contraction of the steel in the heat. There's a lot of movement there. Remember when they put the last piece of the Arch in St Louis together they had to apply ice because they were running late that day and every degree in temperature changed the size of the unit.
Up here in north Texas we have some of the worst of the expansive soils. I've fought it since I arrived. What I try to do is not have the ledges on top. I also make sure the holes are free from loose dirt when I set my posts. Loose soil will pack and shrink when wet and the post will sink. I also make sure I'm not drilling cone shaped holes. That gives the soil leverage when it comes to pushing the post up out of the ground.
I don't get leans in my fences. But I still get up and down movement. It drives me crazy but it is what it is. Where I'm building the barn by myself there's hundreds of feet of ornamental iron fence that I built seven or so years ago. It's put together as prefabricated panels from Payne Fence attached to posts with brackets and screws. The fence is still nuts on for straight and height. The soil is sandy loam and doesn't move.
As for your problem. You could come along with a twelve or sixteen pound sledge and smack the bejezzuz out of the posts a couple of inches above the concrete. That will break the concrete ledge and remove that. I'm not too sure about the putting the sand in the gaps you have around the posts now. That's because when it rains and the ground expands I can see the sand acting as a lubricant enabling the clay to lift the post easier than before.
Braces and anchors can't be put on the inside because they present a hazard to livestock. You can't do it on the outside, first because it's in the right of way and it isn't your land. Chances are most likely anymore there's buried utilities in the right of way and you damage one of those and you're in trouble.
What you could do is rent a jackhammer or tamper with a compressor. I would start in the middle of the line and pull one post straight. I would tamp or jackhammer the existing soil down as far and as tight as I could. The engineers will tell us if my idea of using the soil there is the right thing to do. I think it is.
When that post is finished I would move over to the next post and repeat it. The third post done would be the one on the opposite side of the first one completed. I would go down the line alternating like that until the line was finished.
If you decide to follow my advice and you're chewing up nails and spitting out screws as you do so consider the fact that farms in the east that have been farmed since the seventeen hundreds will occasionally have a big boulder appear in the field. Daddy Dirt doesn't like foreign objects in his playground. Your concrete footer is not unlike that big boulder. Daddy Dirt will work to remove it. Especially if Daddy Dirt is an expansive soil.
At least as much as problems can go away with having horses. Of course I might be off base and you don't have any!
