This work introduces two methods which extend the non-convex minimization problem arising in phaseless (NF) far-field (FF) transformations. With the new extensions, knowledge about phase differences between measurement points can be incorporated into the minimization problem. The additional information helps to avoid stationary points of the minimization cost functional which would otherwise compromise the result of the near-field far-field transformation. The methods are incorporated into the Fast Irregular Antenna Field Transformation Algorithm (FIAFTA), analyzed and compared. Their effectiveness is shown by transforming synthetic near-field data sets with partial knowledge of phase differences to the far-field.