I redid some PA tests:
I hope that the H-probe was between the pancake coils (as much as it can be) and did not move between the tests. If it moved - ignore most what I wrote below.
1) naked pancake coils powerd by the PA.
The two peaks that you have marked are to be expected. One is due to SRF of the coils and the other one is due to their mutual inductance and is described in that e-book. I am attaching an excerpt from it below.
Note, that you are measuring the amplitude of the H-field generated by these pancake coils, and it is a measure that is unencumbered by any parasitic and imperfections of the coils and driving circuit. In other words, this H-field is the field that the protons in the water will be subjected to.
Anyway, look at the amplitude of the H-field at the target frequency of 4MHz. To me it looks like it is -13dB. Notice that this is
the highest amplitude of all of these 3 tests !!!
2) pancake coils powerd by the PA, through a symmetrizing 1:1 balun and the parallel cap (Smudge's style).
Here you added the balun and parallel caps and the appearance of peak 1 @4MHz reflects it (the other peaks hove shifted slightly by inconsequentially), however the amplitude at that peak is only -34.47dB, that is ~21dB lower than with the naked coils ! 21dB less power means less than 0.001% of the H-field amplitude you had with the naked coils !
3) pancake coils powerd by the PA, and the parallel cap (Smudge's style).
Here you added the parallel caps only and the appearance of peak 1 @4MHz reflects it (the other peaks hove shifted slightly by inconsequentially),
Notice that this peak at 4MHz is much higher than you had in sweep #2 with the balun, but still lower than with the naked coils.
The amplitude at that peak is only -18.62dB, that is still ~5dB lower than with the naked coils ! 5dB less power means less than 50% of the H-field amplitude you had with the naked coils.
So as these test show now, you get the best H-field amplitude by driving the pancake coils directly without the caps and balun. I wonder why... overvoltaged caps maybe?
BTW: It would be easier to do the calculations if you had the vertical units on the SA set to dBmV.