I had the same problem moving from the 2200 to the 3800, and I've only partially worked around it.
The first thing you need to do is switch to a different paper. The 3800 isn't really compatible with Epson Enhanced Matte (now Ultra Premium Presentation) paper. The d-max is weak, and there's a terrible mottling problem in the deep blacks with this paper. Instead, try either Velvet Fine Art or Ultrasmooth Fine Art. I find the latter to be a very good paper when you get a good batch (watch carefully for surface inconsistencies when you get a new box and have Epson replace any defective box you receive) and the former to work reliably well. Also, I believe that Eric Chan has done tests and established that VFA has the deepest blacks of any matte paper when using the 3800. I stopped printing on Hahn PhotoRag 308 when I switched from the 2200 to the 3800 because of low d-max and problems with some of the colors (although others on this forum will dispute this).
As for the low-contrast-in-the-blacks problem, I'd suggest boosting the contrast in the shadows using Photoshop. Also, I had custom profiles made for my printer and the person who did so kindly made me an extra profile which had a slight contrast boost in the shadows. Either way should help, and which you should choose probably depends on whether you've already finished working on most of the files you'll be printing.
The 3800 is a good printer, but it has its quirks when in the MK mode (I've heard a rumor that it was optimized for PK ink). I'm still using it after 3 years, and I almost always print with MK ink, but I had to make some big changes to my workflow when it first arrived.
Scott