A bare hull should turn to port when driving forward with the rudder set to turn to port. It should also drive to port when the rudder is sent over (and we seem to miss an explicit command to reset the rudder midships) to turn to starboard but with sternway on. This should be at roughly the same radius regardless of speed in the absence of strong trim from the rig.
When you set sail balance ahead of the centre of lateral effort the head should fall off the wind, with the balance behind the lateral effort the head should come to.
"Eye of the wind" is listed over a range from roughly the bracing angle of the yard through the wind in your reporting. This is the usage I made - and with the rudder and mizzen stack and spanker all working together to bring the head around I cannot see the head falling off being a reasonable outcome.
The scale of drag from backed sails seems much lower than the drawing of a driving sail, but this is contradictory to my understanding, where the CD max of a cloth airfoil at 90 degrees is closer to 2.0, with the 'filling and lifting' portion of the drag and lift curve being only important at the relatively low angles of attack. CD being relatively flat function of AOA over the 'draggy' portion of 'non lift'.
So when I teleport-turn the ship into the position below, the bow falls off the wind. I believe this is the scenario Lieste is describing as counterintuitive. However, if I repeat the experiment with all fore-and-after canvas doused, the ship turns bow to wind and even tacks itself. So the aerodynamic behavior of the square sails seems to be correct. This raises the interesting question of whether it is possible to tack the frigate while stationary...