I have the
RME ADI-2 DAC which is not the cheapest option at about $1k, but measures exceptionally well and has all the features you require (I believe).
The thing I find particularly useful with it is the on-board DSP, which allows you to set your own EQ curve for a particular set of headphones and/or for bass management when used as a preamp via the RCA or XLR outputs (you can save multiple settings for multiple different outputs).
Another useful DSP feature is level-dependent "loudness", which can be used to boost bass and treble increasingly as the volume is lowered below a certain user-defined level (or can be disabled of course).
Output impedance is under 0.5 Ohm and it puts out up to 10 V depending on load impedance.
Which particular headphones are you using?