That pick attack sound happened to me when i raised the d-activators in one of my guitars. Try lowering the pickup a bit. D-activator and other pickups behave like that when they are to close to the strings and produce some squeaky shit . The TS may be boosting that characteristc of the guitar and that's way you hear it with the TS on. Try that and let us know if you solve the problem.
That's quite interesting thanks a lot. I'll actually try with a different guitar first, see if I hear the same thing. Was so convinced it was something else (the amp, or the OD) that I forgot it could be the guitar.
Thanks!