re: Replacing rotten posts in overgrown fence line

Are you going to be working by yourself?
If you have help, it's pretty easy to pull up the old fence posts, using 2 old shovels with the points worn concave then sharpened.
Me and my neighbor do this routine pretty often. I'm mid 60s and he's mid 80s.
Then you should be able to re-auger into the old location pretty easily.
We can usually get 10 or 12 posts changed out in a day like this.
I don't know much about those tallow trees though, we don't have those. Plenty of other tree roots though.
We use the auger on the 3 point hitch on an old 50HP JD tractor and it does just fine.
Luckily, we have plenty of cedar available for new posts.