Warm, lush and dark ... Dac up to 1.2K

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.

The Line Magnetic has been discontinued; according to Jeff Halpern, US distributor, LM may be coming out with a new DAC later this year

Might want to look at some of the MHDT tube DACs. They would fit the bill sonically and fit in the price range.

+1 MHDT DACs.