i was in a similar situation and I can say the right DAC will definately improve your sound. What I found is a good DAC takes the edge of digital formats and seems to give a greater three dimensional sound stage that typically comes from vinyl. I bought a Reimyo DAP-777 that was more than you were looking at and have loved it for years. It is the one thing I have not changed over the last few years. I would look at a Birdland audio Odeon-Lite DAC. You can get them for about $400 to $600 used. A real value since they are not in business anymore is a California Audio Lab Alpha DAC that you can get for $400 as well. Good luck.
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Something like the Poth Audio Dac Ah $175 shipped would eat the stock Denon for breakfast. Hearing the difference would be VERY noticeable. If you don't hear the difference for the better. There's a bottle neck some where else in the system. Going the Dac route will allow you the ability to listen to multi-channel through your multi-outs on the player without interfering with your 2ch through the Dac. Some modders do away with the multi-channel and concentrate on two channel performance when modding players.