Update:
No, I didn't have printer color management turned on. (except for trying to see if it helped - it didn't.)
The icc profiles are the latest available from Epson, which means they are about 6 years old, same as the printer. (Does anybody know where to find profiles for the new Epson signature papers for the 4000?)
What I did have was split toning enabled. I had not tried to do any split toning, so I hadn't touched any of the sliders in that block, but the prints on matte paper looked like the saturation sliders were up about 10 units. I still think I see some tint, but it is much better with split toning disabled.
Alan