After using up x, y, and z axes, and the 4th inductor has to reuse the x axis, what should be the polarity of the 4th coil? Should it be the same as the 1st or opposite?
Changing the 'polarity' (actually phase) of an inductor won't help, because coupling between crossover inductors is undesirable regardless of the signal phase.
Place the 4th one in the same axis as the furthest away of the existing three.