Why does the effective reluctance between two windings change?
The mutual inductance can be found as
$$L=\frac { N_1 N_2 } \Re$$ where \$N_1\$ and \$N_2\$ is the number of turns of each winding and \$\Re\$ is the reluctance of the magnetic closed circuit. 

The reluctance is independent of the position of the windings, it just depends on the geometry of the core (and the core material). Therefore the mutual inductance remains the same.