There's a live thread over on DiyAudio about a DHT SET headphone amp:- http://www.diyaudio.com/forums/tubes-valves/228625-all-dht-set-headphone-amp.html
The stated object in the DiyA thread is ~9vrms into 600R (AKG Sextet), 7vrms into 38R (Hifiman HE-500) and hum <-80dB @ 0.4vrms.
It's wandered all over the place without really producing a design yet, however. It's got an ideological bias too because they want to go with DHTs, which everybody is insisting is driven by the sound, but I think it's just another artificial (mad) constraint. I mean, if you want a tube amp, you want a tube amp, with a tube sound, otherwise build a solid-state one, it's a damn sight easier to meet the specs.
I can get 9vrms into 600R from the 6N6P no problem, I dunno about 7rms into 38R though, @ 7pk-pk THD is up around 8%, but I'd be happy to be driving most headphones, I don't need to cover absolutely all. One thing, 600R might cause problems with the OPT primary impedance getting very high. You could slug the O/P with a resistor, but it will constrain the voltage swing. That's when you start to think about more capable OP tubes.
I think dissimilar tubes is a good idea, I'd be thinking 6SN7 for the gain stage, they have a good reputation in terms of distortion and 6AS7 (6080) or even 6528 (expensive) for the O/P. For the moment I can get away with 1.5A for the heaters. If I went to 6AS7 O/P I'd have to rethink the whole transformer issue, not just the PT, which is not a big problem, but the OPT, since the tube has a radically lower Ra.You could get 5~6W with a 6528, I would think, if you went for a bit less you might still get away with one of the Hammond Universal series underdriven using the 32 ohm tap, or there's the 1627SEA, 30W, only 144 euros each. That'd start to be a real luxury item.