Your problem is most likely caused by too long exposed core past the bridge witness point. I had the same problem with Conklin SIT strings on my 7-string (Link Removed).
Longer exposed length and greater difference between full gauge and exposed core both messes up the harmonics alignment. String sounds like crap, and crappier the farther up the neck you play.
Longer exposed length and greater difference between full gauge and exposed core both messes up the harmonics alignment. String sounds like crap, and crappier the farther up the neck you play.