Total brainstorm from a not very well informed guy:

Leverage 2 things, that America has a competitive advantage in:

1: Technology
2: Higher Education/Research

There has got to be a way to leverage science and technology to come up with a way to genetically alter the mussels so they can't reproduce or eat or attach themselves to pipes or something like that. Or, as Matt said, create a surface they can't attach themselves to on the pipes or intakes. Or create something that when they filter feed on it, it kills them or otherwise harms them, but doesn't affect anything else in the lake.

Science and technology should be leveraged to find a safe way to kill or otherwise mitigate the mussels from growing, eating, reproducing or living comfortably. That would solve this. Not easy to do, but I mean, we seem to be good at making things extinct and go away with our capitalistic ways. I would think we could erradicate something pretty easily.

One other thought:
Do they taste good? Is there a market for selling any part of them? Can they make cat or dog food? Can you make vitamins out of the shells? If there is a use or by product, someone would likely pay to harvest these things for some use...

MP