I just received your package of prints, thank you- they are very helpful to review. After examining all the prints you sent, I believe you are experiencing slight yellow staining, which is appearing in the highlights of your images and making them appear "warm". This is not related to the Gloss Overprint, paper or curve used, but is caused by some stubborn yellow color ink clinging to the inside of your damper, which is slowly seeping out and causing the highlight areas of your grayscale prints to be slightly yellow tinted/warm. To eliminate color staining, you can do a power clean cycle, few regular cleaning cycles, or print a few yellow purge pages thru QTR calibration mode (as per our instructions in the Articles> Product Instructions and manuals section of this forum). To prevent color staining, color ink can be flushed from the printer's internal ink system by using PiezoFlush before installing Piezography inks, or the dampers can also be replaced (it seems to be more of an issue with older dampers, that are due to be replaced anyway, which should be done every 1-3 years).
Attached are two photos I took showing a range of glossy sample prints you sent. I labeled the side with the paper name and marked each sheet with our pH pen to give you info on the acidity of the papers you're testing (purple is neutral/archival, yellow is acidic/not archival). I realize it's not as easy to see in a photo as it is in person when examining prints, so I will also explain what I see when viewing and comparing the actual prints. I am a little confused that you referenced Type 5 as the warmest, but Museo as one of the most neutral, as I am seeing more warm/yellow tinted highlights in the Museo print than Type 5. I think the prints on the Exhibition Fiber and Red River papers are the least warm, and I prefer Exhibition Fiber due to the acidity of this Red River paper (though I like the way this paper looks otherwise).
I am in the process of compiling a binder with printed samples on a range of papers from different manufacturers. I carefully evaluate each paper for both color and Piezography printing, and rate them on a range of qualities including surface, pH, marring, bronzing, glossiness, flaking, dMax, etc... Tomorrow I can review my paper evaluations and give you some feedback regarding papers I think you may like to try that will give you cooler results that you're aiming for.
Please let me know if you have questions/feedback, or if there's anything else I can help you with.
Best regards~ Dana