I have a tea olive -- I believe the botanical name is osmanthus fragrens --
which I keep in a large container because it is far out of its natural
habitat of the deep South. This bush normally grows to small-tree size, but
of course that's not possible when it's in a container. I have to bring it
inside for the winter. After several years it has become rather sickly.

I suspect the roots have become choked. I wonder if I might just take it out
of the pot, prune the roots, and replant it. Of course I would severely cut
back the top growth as well, to perhaps a foot or two above the planting
level.

Is this a good strategy? What time of year should I do this root-pruning?