I've had what sounds like the same issue with flats. My tuner tells me I'm in pitch, but I swear I hear "overtones" or something. I also hear differences in volume between the strings, with both problems most noticable in the E string.
I went back to "half-rounds" and the problem mostly subsided. I should probably try another set of flats - I don't recall which ones I had this problem with...may have been DR.
I hate the way the half rounds feel - they really grab some meat off your fingers and they squeek, alot. Once you get used to flats it's tough to go back. Fact is though, the sound is the more important thing....I think!!
good luck...Joe
