Interesting results, F6FLT.
There's a whole class of devices called magnetic modulators that were used widely for FM before transistors came along, and most depended of cross saturation of a core. They wouldn't have worked if your results were the whole story. So how to account for the well known cross flux effect, and also your result?
I think it's possible that your very powerful permanent magnets (relative to the size of the core), have taken the toroid into the little-known regime called 'flux clamping'. This is a region of magnetic operation where the resultant B vector of the two magnetic fields is always above saturation, and there are no hysteretic losses.
The attached patent, one of several from Lipkin, assigned to Sperry Rand, explains the matter better than I can. On page 4, col., line 44 he says:
"As the scalar value of the magnetizing field increases above that required for complete saturation, experiment shows that the saturated flux vector
comes increasingly under the dominance of the resultant magnetizing field, and although the saturated flux changes little in value, it becomes to a greater and greater degree aligned with the resultant field until the two representative vectors may be thought of as locked together.
In the region beyond the maximum rotational loss, an increase in applied field tends to bring the magnetic field closer to saturation. Under a condition of substantial saturation, the field and flux vectors have substantially the same direction, and, as the field vector rotates, the
flux vector tends to rotate with it continuing in the same direction as the field vector. At lesser values of the field, the field and flux vectors have somewhat different directions and the angle between them may vary. This characteristic of the substantially saturated flux vector having substantially the same direction as the field vector is termed "clamping action between the flux and field vectors
B and H” in FIG. 1 and similarly elsewhere in this specification and in certain claims."
This immediately suggests ways to both increase the maximum power density of transformers as well as reduce their losses, but the information seems to have been little used except for several patents from Krause and Delvecchio, originally assigned to Westinghouse. For instance:
https://patents.google.com/patent/US4595843A/en?oq=4%2c595%2c843I'll quote only the patent abstract here, which is a good synopsis of the above principle:
"A transformer utilizing a rotating flux for saturating the entire core. The transformer uses a core configured such that a vector sum of the induction produced by two windings in the core rotates through 360°. This is accomplished by arranging the component induction vectors to be perpendicular and the source voltages associated with each of the component induction vectors to be 90° out of phase. If the inductions are of equal magnitude and the vector sum is sufficient to saturate the core, rotation of the vector sum saturates the entire core and the transformer experiences a very low or nearly negligible hysteresis losses. Various topological configurations for the core, including a toroid, are described. The transformer windings can be arranged for single, two-phase, three-phase, or multi-phase operation."
In terms of your experiment, I suggest if you used ONE neo magnet and brought it close to your toroid while in operation, you would see the standard effect at some point. You're using TOO MUCH PM flux to see the typical orthogonal flux effect.
Fred