More expensive DAC the answer?

Addressing the digital question only (amps & room treatments are worthy side topics, as others noted)--I found a very large increase in my appreciation of digital audio just by ditching delta-sigma DACs and going to multibit, especially NOS (non-oversampling) multibit. After doing so, all that subtle harshness, hyped transients, and shallow 2D note bodies are pretty much gone; music has its true weight & impact restored. The cheapest really good sounding NOS DAC I know of is the Audio GD R2R 11, a combination unit (DAC + headphone amp). You can easily use it as an amp only, however, using USB input/RCA output pair to preamp/amp. You'd get one of the most praised inexpensive NOS DACs around + a bonus (and rather good/strong) headphone amp--for <$300. Just sayin'...

correction: "You can easily use is as a DAC only, however..."

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.