I suggest that you get a good integrated amplifier such as a Musical Fidelity or Arcam or Creek.

IMO any of those will sound MUCH better than your Yamaha.

I suggest a separate DAC, because the amp will be quieter with the DAC circuits located elsewhere; not in the amplifier chassis.

Commsysman's advice is solid and you would not go wrong with an integrated amp from those three companies. In general, I agree with commsysman's opinion on an external vs internal DAC, however it seems Class D amps are less susceptible to that interference than class A/B amps. Both the D 3020 and Nova 125SE are class Ds.

A few other options -

at $499, consider a Marantz M-CR510 from Crutchfield. Its sister unit, the M-CR610 is a Stereophile recommended component, just like the NAD D 3020. The primary difference between the 510 and the 610 is that the 610 has a built in CD player. The Marantz is a "Network" receiver and has streaming Spotify and Pandora built in along with apples AirPlay. It is awesome. I have a CR510 in my bedroom instead of the NAD D 3020 because the feature set is far superior. For the money, it sounds really good. It is a Class D like the 3020 and is part of this new group of Class Ds that have come out in the past year that sound fabulous. One of the guys in the WhatHiFi Forums bought this to replace his Marantz PM6004 which is a very highly regarded integrated amp and said it sounds exactly the same.

If you have a bigger budget or want a bit more power, an integrated with an external DAC is an outstanding option. The Peachtree DAC iTx is excellent at $299. Paired with a Music Hall 15.3a at $550 would be a modest step forward from the Marantz. This is a traditional, class A/B integrated.

My next choice would be the Peachtree Nova 65SE. Another one of these next gen Class D amps that are shockingly good sounding. The Peachtree's all have a slightly warm sound like Marantz. At $999, it sounds amazingly good and is a superb unit for the money with plenty of power to drive those Dalis.

A clear step forward would be a Rega Brio R at $899 with the Peachtree DAC iTx. This would be an amazingly good combination. Ultra detailed yet neutral and balanced. I have a Brio R paired with a Marantz network player driving a pair of Revel Performa3 M105s. The Brio R is THE integrated to get in the sub $1000 range in my opinion.

If you are going to spend more then $1200 (Rega + DAC) or really want the extra power, the Peachtree Nova 125se is a superb choice at $1500. It gets a Stereophile class B and deserves it. I have spent a fair amount of time listening to it while demoing speakers. Peachtree makes an awesome product.