Is the HA-160 capable of driving 600ohm headphones though?
I can't say for a fact as I know it goes up to 500ohms.
Burson HA-160
Because, I could purchase a quality DAC/ Amp and hit all birds with one stone, wouldn't that be nice! 
I checked out the Audio-gd DAC/Amp gear but went with the HA-160 for it's quality of sound and again, from what I've read in the past, the DAC on the STX, for the price, can't be beat. And if you do try to beat it, you're in the thousand USD class of DACs. For the price, I don't think you could beat the overall quality of the Audio-gd "Fun." And the combined price of the Audio-gd "Fun" coupled to an HD-650 works with your stated budget.
My going with the HA-160 over the Fun better fits my intended upgrade path;
STX > upgraded power supply unit > HD-650 > custom headphone cables > HA-160 > NuForce Blu-ray player.
In the end, it's all going to come down to personal choice, personal use. For straight computer use, the STX can't be beat. Equaled, maybe but I don't think it can be beat. In the case of headphones and separates, I'm looking at the NuForce OPPO BDP-83SE Blu-ray player as doing so hits the middle ground smartly. For the price you get double upgraded parts, a Blu-ray player, SACD player and a CD player coupled with a top end DAC. The HA-160 marries up nicely with the NuForce Blu-ray player. Not a bad toy combination for the man cave.