Phew! Big job moving that fence!
My Wheatheart post pounder would make quick work driving new 8'L - 8" dia posts.
You're probably looking at an 8' dig radius, down 3' and then building some kind of motorised circular saw blade attachment for the hoe... can't cut the roots with a chainsaw or an axe, that'd be too easy!
That'd be a good sized job for the JD850, good luck with your lil kitty cat, don't break it.