Just throwing this out there. Check into cutting the lilies off below the water line by using a ween razor or something similar. I think you might be able to control them if you did that on a monthly basis. I believe you might use up the "fat" reserves in the roots, and starve them to death if they can't replenish the reserves. It would be labor intensive on a monthly basis, or even more frequently.
You not only have to deal with the rizhomes, but the myrad of seeds that are sitting on the pond bottom waiting for conditions to be good for them to sprout.
I think I'll just save up the money for the whitecap treatment if you guys think that's going to wipe out the lilies.