DC is very bad for small headphone coils. There's a couple of ways to protect against this - DC blocking filter and short filter as part of the output filtering if you don't trust the DAC fpga programming or use a digital filter implemented in the fgpa as part of the noise filtering to remove non-sine wave components.
Aware of the issues with it - I've built over a dozen different opamp based headphone amplifiers - but this looks like it has a lot more potential if things go wrong DC wise to fry headphones.
btw have you looked at this?
https://www.audiophonics.fr/en/diy-...e-xmos-xu208-32bit-384khz-dsd256-p-14179.html
Not seen it before - interesting bit of kit.