A33, thank you for the reply.
The data in the PDFs illustrate both the ITU and NTIA requirements from four decades ago for antenna designs to be able to select satellites spaced at 2 degree separation. This is in order to receive a signal without co-channel interference from an adjacent satellite, but more specifically to allow an antenna to transmit and not cause interference to other users. In RF theory, this is reciprocity. For the same frequency, an antenna's performance for RX and TX should be the same on paper and very close in reality. The roll-off graphs show the maximum signal strength allowed in order to maintain 2-degree compliance. The graphs start at 1 degree off the boresight. This is important because 1 degree to the left and 1 to the right is 2 degrees (a.k.a. starting at 1 degree on the graph is not arbitrary or "magic").
For a 3.0 m reflector, the gain is roughly +40 dB for C and +49 dB for Ku. The -3 dB beam widths are 1.75 and 0.55 degrees, respectively. At that beam width, you have lost half of your signal strength. The ITU/NTIA calcs are based upon ratios of diameter and the signal wavelength in use. For our purposes, to hit the 2-degree requirements, the resulting equation is "29 - 25*log(theta)". The equation can vary based on a couple of factors, but we will use this to ilustrate the point. Even if we used "32-25*log(theta)", the results are still range-bound.
For Ku, if the gain is +49 and the beamwidth is 0.55, then at 0.55 degrees off the boresight, the gain is +46. From the equation, at 1 degree off the boresight, the maximum gain allowed in order to be 2-degree compliant is "29 - 25*log(1)". The log of 1 is zero, therefore the max gain is 29 dB. As a result, we essentially have a -3 dB drop in the first half of a degree and another -20 dB drop in signal strength in the next 0.5 degrees. That is 1/100th the signal strength when you are 1 degree off the boresight. That is the signal falling off of a cliff. Even a 0.7 m elliptical is still around +37. At this point, if the anecdotes are that adjusting the focal length positioning of a C or Ku LNB can tweak the signal strength 1 or 2 dB, those values are rounding errors when compared to the roll-off values.
We have very differing commentary throughout the years on this site and others about the performance of Ku side car LNBs. There are some talented people who can make it work and there are some talented people who cannot make it work. Skills being considered equal, the only logical explanation to me is that some people have 2-degree compliant reflectors and some do not. I will suggest those who cannot make the side car work probably have compliant antenna systems, while those can make it work do not have compliant reflectors. If we take the anecdotal "it makes a 10-foot dish perform like a 4-footer", that means the effective gain needs to be around +40. If the side car is located 6 inches off the boresight on a reflector with a 48 inch depth, this corresponds to arctan(6/48) = 7.1 degrees. At 7.1 degrees, the maximum compliant gain is 29 - 25*log(7.1) = +7.7 dB. This is approximately -41 dB lower than than the peak, essentially 1/10000th the signal level. This is how antenna systems designed to the 2-degree criteria can discriminate between adjacent satellites. The roll-off has to be that steep.
For your Triax, I will assert that the mechanical equation and associated physical design of the reflector has multiple focal points that where the signal intensity is such that a lock is achievable. For me, it reasonably follows that the reflector design cannot be 2-degree compliant. If the roll-off graphs were followed, you wouldn't be able to lock on those adjacent satellite positions. I can play side car games with stamped 1.0 m metal reflectors that are a bit more challenging with my 1.0 m fiberglass Channel Master that are almost impossible with my 1.2 m TX-compliant Prodelin VSAT reflectors. I am willing to be that no side cars would work on my client's 4.5 m VSAT earth station antenna. They already get calls from the Eutelsat NOC when one of the remote BUCs runs consistently hot on its TX power because the operator is so concerned about interference on their own satellite, nevermind to adjacent satellites.
In the 86-196 PDF, the authors say in Section 2.1 "There are numerous companies that design and manufacture the smaller diameter (3 to 6 m) antennas that exhibit a wide range in the quality of performance... Some antennas are manufactured without the benefit of a full range of technologies and facilities necessary to achieve a high quality product... Performance tradeoffs often favor low cost rather than high quality. This compromise is especially common in the highly competitive, low cost, high volume production type of antenna... In the design of larger and more expensive antennas, such as INTELSAT Standard A and B antennas, performance has generally been more predictable and in line with specified sidelobe envelopes." Those observations were written in 1986. From my standpoint, Section 2.1 is very illustrative and I believe the points have continued to be true through the decades.
Aside, today I was given some old Chaparral prime focus Ku feeds with scalar rings and some 4-leg mounting plates sized for the Ku scalar. They were used to retrofit C band reflectors to be able to receive Ku Star Choice here in Canada. The scalar would press-fit into the mount and used no additional fasteners, so it could only be adjusted "so much". It is definitely not "magic". At this point, I really want to get my salvaged 3.0 m antenna up to do some hands-on investigation.
As always, everyone else's mileage may vary.