Hello CT-55555,
AAT principle is to change the resonance frequency of the antenna by changing the parallel cap connected to the antenna. With a cable (single ended with cable topology) in between this is not possible, because only the matching circuit for transforming from target matching impedance to 50Ohm is on the same PCB. The antenna is most likely on another PCB.
It would be possible if you have an additional line and VCC's (voltage controlled capacitors). You could then adjust the 50Ohm matching of the antenna itself (similar like on the differential matching).

You could also AC / DC couple the VCC controll line and NFC signal on the coax cable and extract it on the other side again. ( NFC Signal = AC, VCC bias voltage = DC). But the VCC signal must be filtered quite nicely i guess, otherwise you could get issues during FCC testing.
The Equivalent circuit of a coaxial cable looks like this:

Which I think is causing the un-symetrical wave shapes if also the shield is driven with the NFC signal.
I did not yet have time to run some simulations about that, but the signal line has R + L in series, where the shield does not. So my assumption is, if you have a differential signal on both of the lines, the impedance of both lines are different and the sinus signal looks different (not differential anymore) on each line.
br Travis