I am in the same situation, hobbyist who needs to play with headphones. I used a lot of different modelling gears and they are very good at reproducing sounds from professional amps. Anyway, as for your post, you know everything about what is good in them. In the long run I got tired from them since I wanted to create my own sound instead of having many and confusing sounds. I tried some tube amp with emouleted headphone output but did not work either. So I am now using a studio tube amp (class A amp with 3 tubes in the pre and 2 in the power amp) and I finally understand "the magic" of the real tube amp.
Regards
Carmine
Regards,
cm