After consulting a few fix-your-own-printer web pages, I've fixed the problem, at least for today : )
The problem was excess ink not draining properly from the parking station, which I've blotted out with a folded paper towel. Well, with six or eight paper towels, actually. And I'm getting a bottle of Epson head cleaner to loosen the clotted ink up on that parking mesh.
Then of course, my print heads were totally junked up, so following web advice -- hey, they're never wrong, lol -- I hit the button to unpark the heads for a cartridge change and imediately pulled the power card as soon as they moved from park. Then I took a half sheet of paper towel folded several times, put it in the bottom channel and pulled the print heads over it. Talk about dirty!
But the good news is that the print heads apparently haven't ben ruined, and the iimages are printing fine once more. Now don't try this at home -- I figure if I had folded the towels one more time, the print heads would have been ruined, lol. The instructions did say to set the printer for thick paper if that option exists -- and it didn't.
Thanks to all for the comments,