Polarization is for the transversal fields. So in the far field at 1m away, it is purely transverse wave. Therefore you can use the above defintion to quantify the polarization.
In the not-far region, does it have a defined propagation axis? if so, you can use the conventional definition. However, it is from the wavefront, not for a space field. eg, it is not meaningful to have the circular polarization that depends on the location.
If you believe the fields calcualted by farfieldexact3d can be considered as far fields, you can covert ExEyEz into Etheta, Ephi. Please refer a book in advanced electromagnetic fields to find the formula.