"Been there, done that. The floor heaved because you're in a part of the world where it freezes, and snows. I know it doesn't freeze deep where you are, but any is enough to heave - here's why... The buried 6x6's aren't being pushed up from being frozen under, the frozen ground is gripping around them right at the surface. The ground freezes hard there, as the roof keeps the snow off. The snow outside insulates, and the ground under the snow might hardly be frozen at all. But the ground inside gets no snow, but is still cold, so freezes hard. As if freezes, it grips around the 6x6, and lifts is as the ground expands. Over the winter, while the post is being held up by the good grip of the frozen ground, the space under the base of the 6x6 at the bottom of the hole fills in - because the ground is not frozen down there. Once filled in an inch or two, and spring thaw, the post cannot settle back, so new height (heaved). That repeats year after year. I built an airplane hangar, and used the backhoe to bury the posts 6 feet deep - they still heaved! Then, I figured it out, and fixed it forever....
One inch below ground level, put at least 2" thick styrofoam insulation at least 3 feet diameter around the post. Then the ground cannot freeze around the post, and the one inch which can is not enough to grip the post. With the insulation, the ground will not heave and the no longer gripped post cannot lift.
If the winters have lots of snow, but are not well below freezing, the ground might not ever heave under the snow, which is why some posts survive the winter. That said, lots of big fence posts heave. I see big rocks placed on top of the post, that won't help - the frost grips and lifts, and the hole fills in over the winter.
I now insulate around/beside everything bury, or otherwise want to remain at the same height. Since doing it, I have not had anything heave at all.
It won't fix your existing problem. But, once you figure what you're going to do to level the barn, insulating will prevent frustration several years in the future! For my hangar, once I insulated around every post, I then jacked the beams off the tops of the higher posts, and trimmed off the top of the post, so the roof would settle back to the correct height. A fair amount of work, but it did work. Good luck....