I had the same problem (the twang like a sitar). Simple noodling with a .010 nutfile cured it. Also, you might need to adjust the nut slot height for intonation on that model, I had to.
Yep, if by putting your finger on the string at the back of the nut and the rattle stops then you have identified the culprit, do you hear it through the amp or only acoustically.
Sounds silly, but don't have an amp yet--hoping for one later this month for my birthday. Used grandson's while he was here but for some reason he took it home with him--kids!