You're going to be hard pressed to find a good contractor that's willing to do a job like that.
It's WAY WAY WAYYYYY harder to knock out posts, replace in the exact same spot (panels are built to size) and make look remotely decent then it is to just redo it from scratch and offset existing posts by a foot.
I was in the deck and fence industry for a very long time and everyone who is good is busy right now and if they're willing to take on the job then they're going to just charge as much as building new.
Just rebuild the whole thing, posts usually hold up for at least 10-15 years, so if they're rotten/tipping that's a clear indication the whole fence needs to be done.
We stopped checking for monsters under our beds when we realized they were inside us.