The basic approach when the soil is bad is to bare-root up to half of the rootball. If the tree is too weak for that, bare-rooting a pie-slice - say, 1/4 of the rootball - is another option, as is boring a few holes all of the way through the rootball in select locations.
The idea with these approaches is to get some new soil around the roots to help strengthen the tree. When bare-rooting half of the rootball, I’ll usually wait 2 years before repotting again, at which time I remove the rest of the old soil.
Even if you can’t bare-root at all, simply working around the edges of the rootball and surrounding the rootball with new soil will help the tree gain vigor, though the bare-rooting will still need to happen down the road.
When bare-rooting half of the rootball, I usually start with the half that has the least amount roots, or, if the rootball is fairly even, with the front half (a trick from Boon as it’s easy to remember “always start with the front half”).
A couple of examples:
The tree in the article you mention may have good soil at the center of the rootball. If so, often the circling roots at the bottom can be removed and the tree will then fit back into the pot. It’s common to see white pines pushing out of the pot in Japan as there is reluctance to repot unless it’s necessary. Repotting can reinvigorate a tree and measured growth is usually desired when refining white pines.