I think the problem of field direction reversal is not insurmountable. It is quite likely that the pigeons use other clues as well as a magnetic sense, for example the position of the sun and how that varies.

It may well be like those experiments where they made someone wear a device that turns vision upside down. (The back of the eye normally receives an upside down image anyway and the brain corrects it.) After a short while their brain adapted to see normally. It may well be that the same kind of factors would work with magnetism, that is to say there is a way for the bird to generally know where north and south are and the brain adapts to refine this using the magnetic sense. Therefore, the polarity of the field isn't really relevant just like the upside down or right side up images in the eye.