Relaxed, musical DAC around 2k used?

border patrol!!!! this is what you are looking for when it comes to forgiving and relaxing. Im thinking about getting one as a backup or second room.I have a Lampizator and too is super warm and relaxing, blew the chordette out of the water and has a great warm sound to it. the Lampizator is the next step from the border patrol in value, both R2R

border patrol day can be found used for a little over 1k too so you will save some money

I was looking for a DAC to stand in for a couple of years to go with a Naim Core via SPDif while I waited for their new streamers (which were obviously coming once the Atom etc were launched). I tried a Rega DAC-r and a Chord 2qute, initially with Chord shawline and fairway cables but found the Rega a bit boring and the impressive but too clinical. I wasn't going to pay £200 for a digital cable if I could help it so I'd ordered a Belden 4794R from Blue Jeans for a fraction of the price and along with a BNC to RCA converter, this arrived while i had these two DACs on home demo and it livened up the Rega very nicely, enough that I stopped looking any further. It was particularly rich sounding with filter 3 and conveyed emotion very nicely though it was obviously less detailed than the Chord. I never tried the USB input but it's sopposed to haver been improved over the original Rega DAC.
It's probably best to try to get to hear one, in your setup if you can and try a few different cables of whichever format you use, there seems to be some sensitivity to cable choice so don't assume they're all the same (as I did originally) or that the more you pay the better the cable will perform for your system.

I have aBryston DAC3 which I found to be easier on the treble than my Mytek Manhatten.  Either it or the DAC2 can be found used in your price range

Of used listings atm that I've heard, there's an M51 for a good price (I  still use one!) and the aforementioned Auralic Vega. Also a Metrum Onyx which might be up your alley.