"Best" DAC for a grand or less

Eastern Electric Minimax DAC. This is the one to beat at under a grand...

If the Rega DAC sounds anything like the Apollo CD player, go for it...
The Rega DAC also has XLR outputs!

Burson HA 160D. I was having the same problem with my 2ry system- too bright. I've only had the device for a week so it's not "broken in" by maker's recommendation. Yet already, I'm very happy with the system's sound with the unit in place. At $1100, it's eesentially in your price range- do audition it. Won't win any appearance contests, but fixed my system's digititis.

EE Tube DAC

Killer value and flexibility minus any bragging rights: the amazing and inexpensive Cambridge Audio DacMagic. Try it before spending a lot more for small (if any) improvements. You can always sell it if you don't like it!