DAC for 300-400 $

Have you considered buying an amp/dac combo? the HA-160DS is pretty good headamp and it comes with Dac. Just a suggestion.

ok, I'll bite. I shopped heavily at the same price point.
Schiit, Arcam rDac, Musical Fidelity VDAC II were at the top of the list. I ended up with this and am quite happy.

Valab WM8741 24bit 192k USB DAC --- Dual WM8741 (mono mono configuration) Balanced output
It is now $380 delivered. The Valab has the well known Tenor USB interface, which does 24/96, but is not Asynchronous. I ended up also buying a Lars Audio USB interface that is Asynchronous, uses galvanic isolation on the power supply and processes with a similar chip of the Schiit Bifrost, does 16/44 through 24/192 (thats all i've tried) Excellent build. This has been a very satisfying combination. Rich, textured, detailed, tight and fast.
Good Luck, there is alot of nice gear out there, find the one right for you. Tim

I think you should try a Grant Fidelity Tube DAC-11 or an older DAC-09 with a Western Electric tube in place of the stock one. It can power the Sennheiser HD-650 with no problem and is a great sounding combination IMO.

For just slightly above your price range, a California Audio Labs Alpha would be excellent.

Michael