More expensive DAC the answer?

While upgrading your source will probably give you an improvement, and going to tubes will most likely sweeten up the sound, it sounds to me that you need to work on speaker placement.  Klipsch speakers can get a little shouty, especially when paired with a brighter integrated like the Yamaha.   Good speaker setup is crucial. 

You have to spring for the current model, R-1 (link below), &799 + shipping. That's not dirt-cheap, but it's still way less than most balanced output DACs. 

BTW, Schitt may have something cheaper w/balanced outs. Not sure about that.

forgot link to R-1:
http://www.audio-gd.com/R2R/R1/R1EN.htm

Agree with everyone about the amplification. A tube amp of any type will transform the problem and open your eyes and ears.

Putting those dollars into a DAC is a waste. DACs are a dime a dozen and a commodity with their overall ability for less than a $100 these days. You will discover this yourself. 

Try a decent tube amp and you'll get your answer fast.