Well, last I checked on AgoN, it was a few hundred over your $1K limit. But a
Pioneer DV-AX10 would at least make a hell of a transport.
It's got Analog Devices Multi-bit 192k / 24-bit Audio D/A Converters for the L/R channel out puts. I don't know how they sounds as I've not ever hooked the analog outs up on mine.
But it's a serious piece of hardware (weighs 54 pounds!

). Excellent transport. Better than any other Pioneer deck. And I found it to be slightly (very, very slightly) better than a Proceed PMDT as a transport.