I could he wrong, but I think that attempting to accurately impedance match a near field antenna to a transmission line or device might be somewhat of a wild goose-chase. One may need to just accept that there will be somewhat of an impedance mismatch, and make the best of it.
With a far-field antenna, the antenna impedance depends upon the frequency of the signal, the dimensions and geometry of the antenna, and the natural impedance of space. When calculating or measuring the impedance of a far-field antenna, an assumption is made that conductive or magnetic objects are not moving into or out of or within the near-field.
The impedance of a near field antenna, when in actual use, will definitely depend upon what is nearby, especially, but not limited to, the companion transmitter or receiver. The impedance will change depending upon how far away such objects are, and their electrical characteristics. Move the receiving antenna a bit, and the impedance seen at the feed-point of the transmitting antenna will change.
That may be one of the reasons why you are having difficulty reconciling your calculated impedance with what seems to be the reality. It may not simply be a mistake in calculation, but a problem taking into consideration all of the variables that lie within the near field.
A useful question to ask is how critical is it really, in your case, for the antenna and transmission line impedances to match, and to what degree? What, in your case, are the consequences of a mismatch?
I am definitely not an expert in near field antennas. I only offer my thoughts on the basis of my general understanding of electromagnetics. So, someone with more specialized knowledge may be able to correct me if I am wrong.