At 65Hz, Th S3, you have a particle velocity of 49m/s and the pressure equals >170dB.
Then it should not come as a surprise that the output is affected by nonlinear effects in the horn, this is a very high pressure and a very high velocity.
Considering these numbers, it is more surprising that it actually performs as well as it does.
Numbers from other horn designs show that very high pressures and high velocities are common, and a smaller horn may actually present numbers higher than a larger one.
Also, the area of the horn channel is important here, because a larger area can manage higher velocities (and obviously, higher volume velocities) before separation and turbulent flow occurs along the walls.
I find your Gjallerhorn very interesting; it is extremely loud and powerful, and the powerful driver really works the horn, so that it may be possible to actually measure and find physical limits for this kind of constructions.
Knowing that design of things, and perhaps loudspeakers in particular, are often based on experience and known good practices, one may find that what was valid for horns in the old days may not be true for this kind of design, because the driver is capable of producing a lot more low freq sound due to its displacement capacity.
PA horns can of course be even louder, but rarely goes as deep and the drivers usually have a lot less displacement.
Now it would have been very interesting to see some distortion plots of this one.
Most useful would be dist at different levels, and 2hd and 3hd separately plotted.
(I understand you are working on getting the impedance measurements.)
I have started to look at nonlinear effects in low frequency horns and distortion, and what I can see so far, is that it may not be a big concern, as the distortion from the driver itself will be quite large before the horn itself add significant levels of distortion.
That is, unless you make an unfavourable design - and that is a good reason to search for more knowledge about the subject, so that one can learn good design practices, to avoid building expensive piles of wood.
It also surprised me to see the actual numbers for pressures and velocities inside the horn - very high pressure, and velocities that also quickly enters the range where separation and turbulent flow occurs.
The kind of dist people are so afraid of in horns, often called throat distortion, is not a big problem in bass horns, as the bandwidth of the horn really is not wide enough to allow waves to propagate long enough (in wavelengths).
Talking about turbulence, one can imagine what happens through the horn bends..
I tend to believe some distortion at very high spl levels are not that important, as the speaker should only enter this kind of spl on top of transients, and then the dist will not be detectable as the time span is too short.
I am more concerned about compression.
I think that using practical designs and measurements of those are the way to go.
This makes it possible to verify theoretical hypotheses, and find out what actually works.
I shall not indulge in to this any more here, as the subject is rather comprehensive, and also I do not have much valuable information, at least not yet.