If I understood you correctly, something similar happens with myself. Schematically, it goes as follows: if I have to go from A to F in the following diagram,
A B C
D E F
and I cannot go directly through the rectangle's diagonal but I can go on the squares' diagonals, I will go A-E-F, and return F-B-A. Is this what happens with you?
The mechanism is probably that the brain at A, knowing it has to get to F, scans all immediately available directions to walk and determines that AE is the one closest to approaching F. That the path that starts going to B will have the same total length is a fact available in Far/analytic mode, but not in the mode that operates if one walks while thinking of something else.
Wow, that actually describes a pretty sane heuristic.
Picture a circular road on a map. Let's say that my office is at twelve o'clock, my home is at five o'clock, and the post office is at three o'clock.
Now, suppose I have to leave work, pick up a document at home, and take it to the post office to mail it. I know it's faster to walk clockwise home, passing the post office, and then return to it with the letter. But my gut preference is to go counterclockwise, either because of an aversion to retracing my steps, or because that route just ... feels "cleaner" or more efficient somehow, or ... I can't articulate it any better than that.
Does anyone else share this intuition? Is it a manifestation of one or more known/studied effects?