https://www.reddit.com/r/WC3/comments/4eizph/town_portal_bug_how_do_you_do_this/
I got it! Took me a while, but I got it.
If the TP target location is too far from the tree being portaled to by the time the TP should occur, then it is cancelled. This requires 1. natures blessing, 2. that the tree being TPed to is walking in a straight line, and 3. that the TP target location be manually selected to be as far as possible from the tree in the opposite direction in which it is walking. During the TP charge time, the tree becomes even farther from the TP target location, and an error message appears: "a unit could not be teleported". It appears this can be done over and over without penalty (and no cooldown on TP)...obviously something that should be fixed.
Edit: PiratePree is right. It doesn't require natures blessing, but it does make it easier. You also don't need it to be walking or even uprooted prior to selecting the TP location, but that also makes it easier. You do need to manually select the TP target location to be as far as possible from the tree, and move it in the opposite direction.