So that means headphone amplifier needs to be after NAD unless putting it paraller with it.
Line inputs don't cause any real load so you could certainly use y-cable from E-DAC to connect it to both headphone amp and NAD.
TV is likely to also have some analog out.
Actually If NAD's headphone output has switch which disables/mutes speaker output when headphones are connected that would be better.
No need and sense to pay anything over 100€.
Heck, £120 gets whole USB sound card with very good DAC, and the connections of sound card including inputs maknig it possible to use it as headphone amp.
https://www.overclockers.co.uk/crea...-card-with-headphone-amplifier-sp-183-cl.html
https://techaeris.com/2016/09/29/sound-blasterx-g5-review-amplify-enhance-headphone-audio/
That should tell how much "audiophile" makers charge for single purpose devices.
And Objective2 was designed for "straight wire with amplification" neutrality and being indistinguishable from headphone amps considered reference level in blind testing.
http://www.headnhifi.com/amplifiers
It's available also as DIY kit, myself made two of those some five years ago.
You just don't want to turn gain to high on it with 250 ohm headphones.
Because it was designed to drive 600 ohm Beyers to hearing damage in minutes and some more volume.