Hi Sean, yeah Fall is okay but I'd rather Summer stuck around longer

By coincidence I've just starting trying this paper (on my HPs) for daily use stuff.
I can only offer my random non-pro thoughts... I feel there are 2 main topics here -- the
printer profile itself, and the
workflow -- and the latter is probably more important.
Printer ProfileI looked at it in GamutVision (screenshot attached), and wow yeah it's indeed a lumpy puppy lol

For comparison I've also attached my gamut on the same paper on a HP Z3200PS made with a 1728-patch target and processed in Argyll (and tbh the default 464-patch target is nearly the same). Obviously much less lumpy.
Despite best efforts to linearize printers there can always be some non-linearity in the gamut mapping. And that in itself can be okay because the colour mapping can handle it. But this is the lumpiest I've seen in my limited experience, so I have some speculative ideas.
First you might re-check the printer calibration prior to any profiling attempt to make sure it's in a good state for profiling, plus check that none of the colour channels are having any ink delivery issues.
Next, 3000 patches is a big target. (I can't imagine scanning that sucker by hand wow. I use legacy HP Z-series printers that automate patch scanning.) One of the advantages of a larger patch count is that it can better fit to non-linearities, which can be used to squeeze a bit more nuance out of a printer/ink/paper combo. So gamuts can become a bit more lumpy as the localized fit around those non-linearities gets tighter (think like a vacuum-seal shrink wrap on an irregular object vs just a plastic bag around it). That said, this still appears extra lumpy to me.
So next thought, how long did the target dry before scanning? Because one theory that pops to mind is that the print was still drying during scanning, and this particular printer/ink/paper/humidity combo may be one that has significant gamut "contraction" during drying. So I think a combination of a long-ish scan time and likely jumping around the gamut volume due to the arrangement of patch targets while the colours are still drying could in theory produce a lot of localized lumps.
Now that the target has had more drying time, if you repeated the scan I wonder if the lumpiness is significantly reduced.
Edit: Another silly Q, if the target was on multiple sheets, is it possible they got scanned in the wrong order?

If none of that explained the lumpiness then maybe it's something with the scanning hardware + software process. You could take your scan data into a different profiling software to see if you get significantly different results (Argyll etc).
Once the lumpy mystery is sorted out, you can contemplate whether a 3000-patch target is worth all the effort, on what is arguably a "budget" non-archival non-matte paper on a small CMYK printer. I think many would suggest there's negligible benefit here for the cost.
WorkflowOn the colour management workflow side, this caught my attention:
"
We're hoping to create a profile that requires fewer adjustments when soft-proofing and yields a warmer print that better matches the display."
Maybe I'm misunderstanding but it seems kinda reversed to me. The printer is going to produce what it's going to produce. The soft-proof is just a simulation to try to predict that (under specified viewing conditions), but obviously far from perfect. If one's preference is to produce warmer prints that match better with what's on the screen, that's a
creative decision and I feel printer profiling isn't the tool for that. The printer profile describes the printer/ink/paper's
capabilities so colours can be mapped to it in the best way. If we want to change what a print looks like, then we make pre-print adjustments to the image itself.
You mention setting screens around 5750K. I use D65 since I've read that D65 screen + D50 print tends to make proofing life easier (and it has been for me). Running "warmer" could make the prints seem cooler than you'd like. So you could try something like D65 instead to narrow the gap during soft-proofing. And/or you could apply pre-print adjustments to shift colours warmer, but note the paper white is still gonna be what it is, you can't change that.
In either case, I feel that somehow changing a printer profile to get different results is not the way. Profile the printer to
characterize it, nothing more. Likewise for the screen. Maybe try D65 screen to make life easier for proofing. Then print, evaluate, and try pre-print adjustments to get the print you'd like (can vary from image to image...).
Hopefully there was something helpful/correct in that wall of text lol. Cheers!
