I would recommend the Audio Note kit 2.1 DAC. It is easy to build and has R-2R AD1865 chip (best sounding chip ever) and tubed PS and tube line stage. Very smooth and dynamic DAC.
The cheapest Lampizator dac (Amber) starts at about 1200 euro and they have the sound I think you're after. Audio Note UK (not AN kits) also make excellent "analogue-sounding" dacs but, I think, not in your price range. However, you could probably find one secondhand. Another option would be the Line Magnetic LM-502CA, which would be around $1000 secondhand. All of these offer a non-fatiguing sound with excellent timbre.
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