A QTW cannot take you between two positions of equal distance, I believe
-- is there not some parity quantity obeyed by QTW's (net twist of
the six center cubies)? If so, then there cannot be two positions of
equal distance separated by a QTW, for then there would be an odd
length identity transformation, which would violate parity.
(In the example you gave, there are *not* two positions of
equal distance, but only one -- the halfway point.)