Happily, I was able to bring some outside expertise to bear on the situation, and in a day it's effectively cleaned up. The trick, it turns out, is to take the plants out of the aquarium and run them under cool running tap water until the algae breaks up. Then the plants go into a container of water with water conditioner so that the tap water's chlorine and chloramine don't harm the fish when the plants are returned to the tank.
I did all of that plus an additional water change yesterday. Today the whole tank has a much-improved appearance. And there's a happy bonus.
The disruption to the plantscape means that the fish and shrimp were all unsettled, and the shrimp took to their old roost on the water intake for the filter. With them there assembled, I was able to count one more shrimp than I'd previously known about. I've still got six of the nine that survived the ammonia surge that I had about three months ago. Woohoo!
Consistency requires you to be as ignorant today as you were a year ago.
—Bernard Berenson