I got about a gallon of Java moss just completely infested with thread algae. I agreed to take it knowing about the algae 'cause I wanted to try Flourish Excel on it to see if it would work.
I soaked the moss in a bucket with a double dose of the Excel for a couple days, then put it in the tank I dose daily anyway, at the amount recommended on the bottle. It was all gone (every last thread) within 10 days.
I don't know the mechanism by which the Excel kills the algae, but it completely got rid of mine. And the moss is doing very well, too!
Remember that Darwin was mostly right!