Trying to adhere to the topic:
From the TX viewpoint, for simple circularly polarized feeds one still needs to achieve splitting of the signal into two equal amplitude components with +-45 degrees shifts, i.e. two orthogonal fields from two virtual elements with impedances of 50+j50 ohms and 50-j50 ohms. Parallelly fed this results in a total feed impedance of 50+j0 ohms purely resistive.
These two resonances should be evident from the hardware when measuring with a VNA: there should clearly be both impedances with their relevant resonances, ideally symmetrically about the nominal center frequencies. Accomplishing all this with a simple feed plate, a single feed point and a single disturbance (the screw) is somewhat challenging and tough to replicate in a hardware duplicate. But with very tight manufactureing tolerances it IS possible over a very narrow frequency range (obviously). This is why it is so very difficult to copy mechanical drawings with good overall results. You really need to know what you are doing and also have the instrumentation. Pushing limits, I routinely measure ellipticity on HF in the confines of my small basement - figure that one out 
Once you have determined the apparent crossed polarized fields of your particular CP feed, you should be able to clearly affect each resonance individually (might take a piece of dielectric on a very thin dielectric probe). I usually use small pieces of PTFE, Rexolite, plastic or even just my finger tips for this type of work.
After decades of work with CP polarization for a very wide range of applications and with quite a few years on HF too, last year I finally put together a (quadrature) dual channel polarimeter demonstrator for HF and this spring I also added a dual channel downconverter for 2.4 GHz for demonstration purposes:
https://73.fi/oh2aue/oh2aue_polarimeter.htm
Now, for my tripole antenna experiments I obviously need a three channel polarimeter. Think of this as an analogue oscilloscope CRT with magnetic deflection using external coils (e.g. Cossor 1039 or vintage radar CRT): instead of two orthogonal coil pair, only three deflection coils are needed in trigature, i.e. spaced at 120 degrees. Obviously magnetic deflection if bandwidth limited, but the display is on an arbitrary IF anyway. And I just love the dual time constant phosfors of my radar CRT 
Until now I have been using vintage HP Vector and Constellation Displays with various homebrew 3 phase/2 phase RF transformers and matching three channel coherent converters depeding the on frequency band. This is all very fine for displaying CP ellipticity directly and in real time, but all the way, it is imperative to see also the complex impedances, such as (plot of the three resonances, 0 degrees and +-120 degrees with the total return loss of the trigature hybrid with imbalance load, 5dB/div):
https://73.fi/oh2aue/2400_MHz_…rid_input_return_loss.jpg
The overall ellipticity (linear deflection) of this contraption may be seen in the last plot of the first link.
Michael, oh2aue
P.S. winding of CRT deflection coils is described in detail in the Bell Labs microwave series...
P.P.S. how many multipole antennas can you count in the AO-40 photo on the left?
