Good point. I should have included that information initially.
The two that I'm using thus far are Hahnemuhle's Fine Art Pearl and Fine Art Baryta. For the latter, a glossy, I use the maximum resolution, 2880, print for Finest Detail, and I selected Ultra Premium Photo Paper Luster as the media selection. Of course, I'm printing No Color Management in CS3 PS Extended, and I've turned off color management in the driver.
It's not that the target is light. It's lighter than what I experience on the 4000, which is actually pretty dark. But in speaking with X-Rite in the past, correctly printed targets tend to be dark in appearance. This makes sense, because one wants black areas in the target to be near the maximum black of which the paper is capable. As a comparison, a higher percentage of the patches when printed with the 4000 are quite dark. With the 3880, a smaller percentage of the patches are quite dark.
As for Fine Art Pearl, which is a semi-gloss, I'm experimenting with Premium Fine Art Matte and Ultra Premium Fine Art Matte as my media settings. The other settings are the same: 2880, not fast, Finest Detail, and 2880 resolution. Normally one would specify Photo Black with a semi-gloss paper. But, I've been able to get really excellent, deep blacks with this paper using Matte Black through my RIP. (Deeper than with the Photo Black.) So, I thought that I would give that a try.