You could hook up an external headphone amplifier to the NAD's headphone jack, but not something that I would do, would rather not get into double amping.
I would say it would be better to invest into a external DAC/amp and feed your source(s) into the DAC/Amp.
I just paid $300 for an Audio-GD NFB-15.32 DAC/Amp, comes with USB, optical & coaxial inputs and has a headphone amplifier along with a separate (analog) line-out feature.
Makes my DT990 Premium 600-Ohm headphones sound nice.
I would assume it would bring out the best in your current 50-Ohm HD598s.