Well you'll need a back brace some aspirin and a lot of water. Maybe a crane too and some friends. Sounds like a big job

Not so sure on the 'how' but I do know people do it without too much harm. there is a botanical garden in Corpus Christi Texas that has what I would call a forest of plumeria trees and to protect them during the winter they actually dig them all up and place them in a green house with very small rootballs so I do know its possible.

a 15 foot tree with a small root ball should be around 150lbs. Totally doable. :)

As long as you stake it while the plant establishes roots it should be just fine.