About 25 years ago three catalpa (Indian bean tree) seeds were planted in the Northern Hemisphere in a temperate climate. They came from the Southern Hemisphere and seem may have been from a Catalpa speciosa ("northern") rather than a Catalpa bignonioides ("southern").
Not really expected to grow, the three seeds were planted in close proximity. All thrived, so naturally one fared a lot better than the others, which were held back to different extents. About a decade ago the middle-sized one was transplanted as a 'stake' - about five feet of trunk, of diameter about 3½". About five years ago the smallest was transplanted as a whole tree about 7' tall. Both have thrived since.
The middle-sized one is now about 15' tall and is no longer suited to its location. When I was contemplating cutting it down a neighbour happened to mention he was intending to buy an established tree. He is amenable to a catalpa but without a mechanical aid (out of the question) the 15' tree can't be moved intact. Investigating other possibilities I have seen mention of root pruning. However this has been described as passé in the context of catalpas and the data from a controlled experiment (by the RHS, on beech trees planted 2005-2008) is "yet to be analysed".
The trunk of the 15' tree is around 4-4½" so a root ball extending out to five times the trunk diameter is not practical here, though something like three times might be (for a root ball around 2' across).
Given success with the "stake" I am also contemplating top pruning back to about 10' and anything spreading more than about 3' – which would mean cutting off almost all the branches.
Worse, a time constraint means I cannot wait until Autumn and may have to attempt any surgery and transplanting just at the start of the growing season. I think the chances of success as slim (perhaps so slight even the attempt is not worth the bother) but should I "give it a go" anyway—and what can I do to improve the odds of success, if only by a small measure?
There is a vaguely similar question here: How to transplant this oak tree? but the tree is a different genus and about twice the height.
Transplantation, if it happens, has been put on hold since the prospective new location was not suitable.