See below video on how i tried it, not sure its the correct way, especially the calibration of the "thru" part and to what value's i should look.
Yes H-field "thru" calibration is difficult because you do not have a device that converts constant voltage amplitude (from the VNA) to constant amplitude H-field at various frequencies.
If your VNA had a constant current amplitude output then this would not be a problem.
Take a look at my attempt to do that some pages ago, where I used two identical 10mm shielded loops parallel to each other. In that attempt the constant voltage amplitude signal from the VNA's transmitter obviously was inducing less and less H-field amplitude in the transmitting coil as the frequency was increasing (because the coil's impedance was increasing with frequency), so it was behaving like a low pass filter. The receiver coil had the opposite characteristic. Your H-field probe is flat, because it is compensated internally up to 70MHz. You proved it by clamping the i-Probe on 15mm of Litz wire, which was shorting the VNA's transmitter....or was it the SA's TG ?
Anyway, fudging the "thru" by as a straight-through electric connection and assuming, that the H-field probe is flat, still lets us see the relative magnitudes of the H-Field and it is obvious that the field is the strongest on the middle of the winding (not to be confused with the center of the coil) and at 27.5MHz.
With one coil, the orientation of the H-field probe at the middle of the winding should be such as to maximize the amplitude sensed by it, ...but not so close that the capacitive coupling can take place.
With two coils and this probe between them, its orientation should be radial like in my video, period.
Let's investigate why the H-field's amplitude is so much higher at 27MHz than at 3MHz. Perhaps we can utilize the phenomenon responsible for it to our advantage.
When you cut the coil in the middle (take a look at the photo of my coil where I did it) please use the picopulser, tee, fast scope and 220Ω pot, to do a simple TDR experiment and find out what the characteristic impedance and velocity factor are, when this winding is treated as a transmission line.