l think the STX is a good suggestion (also, the fact that you can upgrade to an external device in the future, should you want to). If memory serves, STX has 'dolby HP', which would be a great pairing with the 700s.
And yes, tubes color the sound. You would use them with the HD-700 in order to smooth the highs (if they bother you or if you simply prefer that 'colored' sound). l'm fine with my amp and the way highs sound out of it (and 700s).
Yes it does have Dolby Headphones.
And with tubes you can change the sound to your desire which might be to your liking, it's not just about "smoothing" the treble.
Also check out the specs on the tube amps some have pretty good specs without any visible/hearable distortion.