Well, my Supra can run the 6bx7 output tubes, so my set-up is a bit different than yours. However, I've used 6sn7 tubes before and can say the more impactful tubes sound better to me when listening to the GS-1000s.
Because I have a warm full source, and the GS-1000s have a lot of bass, I tend to like the 6BX7 output tubes. They are fairly neutral tubes and make the GS-1000s sound really good. I don't like tubes that add much warmth with these headphones.
The other key is the gain tube and I was just playing around with which tube sounds best when my amp blew a resistor due to a bad tube and I've had to send it back to Mikhail.
I did like the 7n7 as gain, but switched to 5687 just before my amp went out. After switching I realized the 7n7 had a bit too much warmth compared to the 5687. I liked the tightness the 5687 contributed, but it seemed a bit brighter than I liked. It was a Tung Sol D-getter. I was going to try a Raytheon, as I heard they are warmer, but didn't get the chance.
When Mikhail sends my amp back I am going to try a 6414 as gain, as the description of this tube sounds really good. I might also try various 12sn7s (Hytron, Tung Sol round plate).
The only thing I know for certain at this point, and my set up, is that the 6bx7s sound excellent as output tubes. Hopefully, I can find a gain tube that complements these, eg. that does not add too much midrange bass and yet sounds natural.