Thanks for your reply, Neil.
Yes, it is the HP Print Utility that was used to generate a Custom Paper Preset for the Harman paper in question, and the resulting prints are the very dark prints I described in the OP.
You'll recall that a paper preset not only encompasses ICC profile generation, but also parameters like ink limits, GE dosing, star wheel position, platen gap, P/M Black assignments and others. Media Type selection is yet another variable that impacts these values, so the type initially selected in the Preset generation process also plays a significant role.
I have begun to experiment with reducing ink limits through the Change Printing Characteristics in the Managing Paper Presets dialog. Ink limits work on a +80 to +120 scale, with 100 being the default. Thus far I've generated two presets with reduced ink limits: 90 and 94. Clearly the prints are better in terms of the original "dark" complaints, but there appears to be some new limitation of gamut and color contrast, just as one might predict in using less ink.