without any answers from us and I do feel bad about that, but sometimes its hard to diag without seeing the project.
Here are afew questions I have for you. are the post pt presssure treated posts? Are the post actually sunk into the concrete footings or are they fastened with metal fasteners like threaded dowels?
Most posts fail about 3 inches from the concrete footing because the footing is not conical in shape to shed the water off and away from the intersection of the wood and footings thus causing rot and premature failure. If the footing is flat or slightly cuped downward, water is holding and causing ponding and rotting.
I guess that you could do your thinking as that would strenthten the fit and buy you some time. But, if the post is rotten then that is your weakest link.
I would personally replace the columns and make the fitting correctly and it would be neater.