A couple of thoughts, no idea if they will help...
A paper's Dmax is partly influenced by the ink density and on the HPs there are 2 "controls" for this, as you probably already know.
The first is the "paper preset" you choose when you add a new paper type for calibration and profiling, it sets the baseline ink limit for that paper. Details are shown in HP's "working with other commercial papers" PDF documents. There's various versions floating around out there but here's one page with some excerpts/links:
http://z3200.com/Working_with_other%20Papers_HP-Z3100_z3200_Printers.htmNote the wide range of ink limits for each paper preset, and also note that only a few use "quad black" printing using all 4 black-based inks (PK, MK, G, LG).
For example the ink limit for the Fine Art Paper More Ink (FAPMI) preset is 60 (the highest available with quad black), while the FAP Less Ink (FAPLI) is 42 (the highest available without quad black). These presets were often mentioned around here in the HP glory days; browse older threads for more info.
The second control is the ink density adjustment in HP Colour Centre which allows +/-20% ink density adjustment from the above baselines. You must recalibrate and reprofile after each change.
The problem with paper presets from paper brands (OMS files) is you don't know what settings they used for them (and ditto for their ICC profiles). Some can be very conservative (such as HP's own). Choosing your own preset based on the info above takes the guesswork out of it because you directly choose the ink limit (as well as the other settings). You can then try profiling with different preset / ink load combinations and compare their resulting Dmax, gamut volume, etc, to select what works best for you (I use GamutVision). I made significant gains in Dmax and gamut volume this way compared to default/canned settings (...up to a point). With HPs built-in specto making it so easy to run tests your only costs are paper and time.
***Note carefully in that "non-HP papers" PDF that you must add new papers via HP Colour Centre first *before* loading the roll in the machine. If instead you try to change the preset type of an already loaded roll it will not give correct results (at least in my experience).
The other topic is the paper itself. I use Ernst Dinkla's SpectrumViz to check paper properties for coatings / brighteners:
https://www.pigment-print.com/spectralplots/spectrumviz_1.htmI don't know if the exact Red River papers you mentioned are in SpectrumViz but based on the ones I found in it it appears that the "Aurora White" is heavy with OBA/FBA (brighteners), so despite being "cotton rag" it's not archival. Its OBA/FBA signature is also very similar to their various "Premium Matte" papers.
Attached SpectrumViz screenshot shows "Aurora Nat" in green, "SoftGloss Rag" in red (both okay), and then "Aurora White" with the big OBA/FBA spike in yellow, and then the various "Premium Matte" papers with similar OBA/FBA spikes.
Ofc OBA/FBA and coatings can make prints look great (for a while...) so no surprise you're seeing significant differences.
So I think there's 2 tasks here: figuring out what the papers actually are (archival or non) rather than what they're branded as; then after you choose some to test, try using the available paper presets in the HP (such as FAPMI, etc) and the ink limit adjustment in HP Colour Centre to hopefully optimize the DMax, gamut volume, etc (if possible). If it's a reasonably heavy paper (~300 gsm ish) you could probably just use FAPMI and call it a day, not even bother with pushing the ink limit higher.
But no matter what you do you probably won't get results on an archival matte paper that have the same pop as the papers with OBA/FBA and/or coatings.
