As a previous Naim owner I can tell you that Naim gear is very “gain rich” with their stuff. I owned the sn2 and an xs2 both with and without flat cap. I found it pairs well with laid back speakers ie older Vandersteen and harbeth etc tried with zu speakers and it will drive you out of the room. I don’t believe klipsch is bright rather very “mid forward”. Not a bad thing but I imagine the synergy is off there with the two brands having the same mid forward sound I can see you would have too much. Klipsch mates well with upstream gear that is softer. All your doing is balancing the wild down to flat and neutral…ie you would have the opposite problem if you paired soft spoken speakers with a lazy tube amp..basically if you like the Naim, change speakers, if you like the speakers, change the amp..good luck!
