Many thanks for all the replies. I think the HE-400 is the way to go. Speakerwise, I prefer a slightly analytical voicing (I own a pair of Audio Physic Virgos), so most probably the HE-400 would make a better choice. As already noted, maybe I should get both, or maybe an HE-300 and an HE-400?
What about amplification and DAC? Do you think a Schiit Vali/Modi stack would make a good choice?