You are on the right track with Tekton, it will be an improvement. And acoustics, depending on the meaning of "massive rug" and how much of the tile floor it covers it may well be too many hard surfaces contributing to the harshness you're hearing.
But my money's riding on it being the AVR. Those things are all pretty bad in terms of sound quality. You already noticed it sounds better with some of the processing turned off. The problem is all those processors and amps and other stuff is still there in the box no matter how "Pure Direct" they want to pretend it is. Pure Direct in a AVR. Good one.
If you want lots of channels you are pretty much stuck with the AVR. But if you want sound quality its pretty easy. Ditch the AVR and surrounds, keep the subs, and get a decent quality stereo integrated amp with Tektons. Whichever ones you can afford after selling the AVR and Klipsch. This will be a huge improvement. At 85dB it will be clean and clear and nowhere near harsh.
But my money's riding on it being the AVR. Those things are all pretty bad in terms of sound quality. You already noticed it sounds better with some of the processing turned off. The problem is all those processors and amps and other stuff is still there in the box no matter how "Pure Direct" they want to pretend it is. Pure Direct in a AVR. Good one.
If you want lots of channels you are pretty much stuck with the AVR. But if you want sound quality its pretty easy. Ditch the AVR and surrounds, keep the subs, and get a decent quality stereo integrated amp with Tektons. Whichever ones you can afford after selling the AVR and Klipsch. This will be a huge improvement. At 85dB it will be clean and clear and nowhere near harsh.