The only HD 600 I can find in the web is one with 300 Ohm, is it that one ?
300 Ohm is not very high I claim it will work fine without distortion.
I have a Digiface USB and it sounds great, never found a problem with some different headphones.
I didn't test with the HD600 but I am sure you will be happy.

A few concrete examples, with which phones you tried, would make it more understandable why you think the combination Digiface USB / HD600 would fit.

@Hammeken:  at the end of the day, best check it out yourself.

With an UFX type of interface I would definitively say no issue as the flagship interface have very powerful phones outputs.
The newer Babyfaces also got more power, there I would "tend to say" that they could also be sufficient for 300 Ohm phones.

But its not only the impedence here which counts and determines the final volume. Also the sensitivity (efficiency) of the phones drivers is important here. Also tastes are different. For those reasons its not easy to judge.

Here some technical data from some manuals. Here you can see how different those values are:

Digiface USB delivers a max output power of 50mW, thats less than older and new Babyface Pro deliver (70+90mW).
UFXII/UFX+ deliver up to 210mW.
ADI-2 DAC / Pro deliver up to 1500mW per channel (unbalanced)
ADI-2 Pro FS R BE delivers up to 2900mW per channel (balanced)

Simply try it out if nobody here has this exact combination that you are looking for.