C.J.
Just a random thought, is it the actual plastic breaking down? Check to make sure these cups are BPA free and check the number on the bottom of the cup. (there is a little number inside a triangle on the bottom) google plastic numbers, there are some that are harmful and are one use plastics (like cool whip containers, etc).
It could be that the cups themselves are the problem. If not, I'd go with the bleach solution.