I typed the message below, then while re-reading prior to sending, thought of something else that could be a huge factor- are you printing form Mac or PC? If Mac, what operating system version, and are you printing from Photoshop or the QTR Print Tool? I know printing from Photoshop on newer Mac OS will cause overly dark output, therefore printing from the QTR print Tool is the best workflow for printing Piezography from Mac.
All your linearizations show overly dark output, though the "MPS-Type 5" output is the best of the four, it is still slightly too dark. I opened your 3880 custom MPS curves, as well as several others I have made for other customers over the years. I attached a screen capture showing several 3800/3880 Type 5 curves I have made for different customers, as you can see they are all very similar, but have differences due to the variances between printers, printing conditions, ink age and condition (if the carts haven't been agitated and printer regularly used to maintain in-suspension pigment, then the output density of the inks is effected, which effects the target print out and resulting curve), etc...
The darkness of the output from this newer 3880 could be caused by a number of factors, including how different machines print and the age/condition of the printer, as well as the age of the inks you're using and printing environment conditions. If the ink you used to fill these carts was from older bottles that had been used in the past, depending on if they were well agitated for in-suspension pigment when ink was drawn out previously, and the storage conditions can effect the remaining ink three years later. Without knowing the exact reason why your output is overly dark from this new printer, you can either have new custom curves made for your current printer (or maybe start with one to try before making more), and/or try installing fresh inks to see if you get more accurate results with the existing curves.
Please let me know what you decide, and how I can help.
Best regards~ Dana