Thank you Mr. MacKinnon:
Did you try the most straightforward (albeit lengthy) approach:
unmerge all of Qt
emerge world and let portage figure out what it wants to put back
There is seldom a good reason to have Qt packages in world (dev packages
excepted) and recent changes in the ebuild have caused lots of mutual
blockers. When I first went through this, I saw that almost all qt-* packages
would be rebuilt on my machines. It seemed easier to restart with a clean
slate. I got a blocker notice which said I had to enable various flags, which
I did and the merge completed flawlessly.