The only machine listed that I have actually heard using phones is the Naim CDS3, coupled with Stax Omega II phones (a combination I own). This can be a quite analytical and dry sounding combination with some recordings. I think a lot of other players would also be brutally exposed by phones like the Stax.
The best I heard my phones sound was with audionote DACs (DAC 5 signature and DAC 4). The Audionote stuff is absolutely grainless, natural and harmonically rich and colorful. It is quite different from the more present Naim gear; my guess is that is an advantage with phone listening.
My guess is that the Linn would sound good too, because it is very smooth and relaxed sounding. I would also bet that the DV-50 would be to your liking as well. It has bass/mid-bass that is a touch warm, and, it too, is quite relaxed in its presentation.
My bet is that the detailed and analytical quality of the EMM Labs gear could be a bit much with some phones, particularly Stax electrostatics.