Here is another attempt at solving the Onitiu problem of constructing a knight tour with 90 degree rotational symmetry on the 18x18 board with the squares in a knight path (the red line). It uses two wazir moves in each quarter, equalling my previous result, making it an Emperor tour.
The pattern is considerably different from the previous example. So perhaps a solution is possible, if the exactly right configuration can be found. Or maybe two wazir moves per quarter is the best that can be done. Maybe someone could programme a computer to settle it.