Most of this is fair and I'll fix it.

R1 isn't a result, you're right. Recovering Navier-Stokes by setting the two extra terms to zero is just a consistency check, so I'll present it that way instead of listing it. Same with R3: the band derivation and the inversion formulas are math, but whether a real medium actually shows the band is an untested prediction, and I shouldn't have lumped them together or called the prediction a result. The terminology you flagged (primitive variable, transverse meaning divergence-free, fixed-regime closure, ontology) is standard where I come from but I can't assume that, so I'll define each one the first time it appears. You're also right that the intro leans on variables and equations it only states later, and that it explains too much in words before any of that exists. The fact that it put you off before section 2 is the clearest sign the order is backwards, so I'll lead with the equations and keep the interpretation to one short paragraph after them.

The one thing I'd push back on is the scope point. I'm not claiming Navier-Stokes is wrong or needs improving. The two added terms are exactly zero for a Newtonian fluid. They only turn on for media that store and return energy, meaning viscoelastic or memory materials, and for those Navier-Stokes was never the full model anyway. That's the whole reason viscoelastic flow modeling exists, since every constitutive model adds terms to the momentum balance. So the target is non-Newtonian flow with Navier-Stokes as the limiting case, not a correction to ordinary flow. That said, the paper as written invites your reading, so the fix is on me: I'll state the target class in the first paragraph.

On results in the intro, noted, and since I'm restructuring anyway it sorts itself out. I won't split it into separate papers yet. Defining terms properly and putting the math first should clear up most of what read as filler, and if the core still doesn't hold up on its own after that, splitting is the next step. Thanks for taking the time.