The uplift force due to bouyancy probably wasn't as much as you may think. Looking at your picture, I'd guess those 12 inch posts are only sticking out of the water maybe 4 ft or so at the normal pond level. Im going to guess your dock is about 20 ft long and varies from about 6 ft wide at the bank and bells out to 10 ft wide at the end of the dock. The space between the decking prevented any bouyancy from air pockets, so the wood bouyancy was the only source of uplift forces. Lets just say that the joists and decking give you an equivalent solid wooden cross section of 4 inches. That gives you roughly 20 cubic feet of wood for the portion of the dock between the first and second set of piers and roughly 27 cubic feet of wood between the second and third set of piers. Add roughly 20 cubic feet for the 24 total feet of piers sticking up out of the water (I am negelecting the submerged portion of the piers since they are waterlogged and probably are heavy enough to be "antibouyant" below the normal water level) and you have a total of about 71 cubic feet of wood contributing to the bouyancy force. Lets just round that to an even 75 cubic feet which is in all probability a huge overestimation. The density of water is about 62 pcf. Lets say that the bulk density of the wood on your dock is only half of that, 31 pcf, (most wood, especially treated wood is denser than this) and that leaves us with a total estimated uplift force of 75 cf X (62-31) pcf = 2325 lbs. Lets call it an even 2500 lb or 1.25 tons. And this force was distribed among the 6 piers, probably a bit unevenly, but nonetheless, spread to some degree among all of them.

As long as the clay "sockets" did not collapse, which I don't think they would since the uplift of the piers probably occured gradually as the water level rost and the voids beneath the piers filled with water as they were created, then you should be able to push them back into place.

As the water recedes, the bouyant force will go down and you won't have to fight back as hard to push the piers back into place. What if you built you a sturdy, but temporary framework out of 2X12's or 4X6's between the last the two displaced piers of your dock and line your frame work with empty 55 gallon drums? Then get yourself a pump and start filling the drums with water. Each full drum of water will give you about 380 lbs of force to push the piers back to their original place. 6 or 7 drums full should come close to overcoming the full bouyant force that caused you all the problems in the first place. As long as the clay sockets are intact, the piers should creep back into place. If that works, it shouldn't be too hard to devise a means of adding enough weight to resist the bouyant forces for the next time a flood event comes around.

If you try this, I would recommend fixing your framework to the piers with one very heavy duty bolt at each pier that goes all the way through the framework supports and the piers. Using only one bolt will allow the two piers to move differentially without putting your framework in as much of a bind and risking buckling or collapse. Keep in mind though, the bolts will ultimately have bear much of the load and need to be really really strong. You could try and build your framework to force most of the load to bear directly on top of the piers as much as possible, but you still will need some lateral support to counteract the overturning forces from the barrels full of water. You could also use concrete blocks, rocks, or other means of adding weight if you have that available. If not, barrels full of water provide pretty cheap weight.

Most importantly, if you decide to try this, I would suggest keeping your distance as much as possible when filling the barrels in case the framework collapses. Fixing the dock is definitely not worth somebody getting hurt over.

Key point is finding a way to get enough weight on the piers to push them back in place. Maybe somebody here can think of an easier, cheaper, or safer way to get 1000 or so pounds of weight on top of each of the displaced piers.....