Had to use both the desoldering and the soldering iron to do this repair correctly, but it's done.
Scoped out the board layout the other day when I checked for voltage at the LEDs. Red LEDs are RD1 and RD2. Green are GD1 and GD2. Blue are BD1 and BD2. See the pattern?
First I replaced BD2, which had definitely died. With it in there, both blue LEDs lit normally, but now GD2 had died. I knew I'd have to replace one of them; I replaced GD2, then tested, and wouldn't you know it but when I powered on again, GD1 was dark. (How much you want to bet that replacing GD1 would have fixed everything? But I had no way of knowing it was the problem.) So I replaced GD1.
Lo and behold, everything works again.
BD1 may require replacing; we'll see how it goes. The green LEDs I put in are a little weak. But it's lighting up red, blue, green, the way it was designed to. Because I am good at fixing things.
Stick that in your pipe and smoke it, Pepsi! You and your stupid three-phase motor test!