I have been very pleased with my JAS Audio Musik 1.2 player. It has a tubed output stage with one 12AX7 in it and another tube is used in the rectifier. The player has HDCD too. The remote is solid and the buttons are easy to find. Sound is detailed without edge, refined and liquid and can be improved with the usual tweaks : footers, electrical isolation and a good power cord. Build is very solid; price is well over $1K but lower than your top limit.
http://www.questforsound.com/digital/dgtl_jasMusik.htm
If you are considering the Benchmark external DAC, IMHO you should also consider the Apogee Mini-DAC, at a similar price or slightly less. These two units do not sound the same and you may find you have a strong preference.
If you do go for a DAC, don't forget to budget for a good cable. There is a very good chance that a 1.5 meter digital interconnect will sound better than other lengths.
http://www.questforsound.com/digital/dgtl_jasMusik.htm
If you are considering the Benchmark external DAC, IMHO you should also consider the Apogee Mini-DAC, at a similar price or slightly less. These two units do not sound the same and you may find you have a strong preference.
If you do go for a DAC, don't forget to budget for a good cable. There is a very good chance that a 1.5 meter digital interconnect will sound better than other lengths.