I assumed you wanted new.
I've owned so much equip, designed so much, sold so much, as an industry member that I've made a study of how people perceive speakers and what clues I could have gotten from those impressions after I've known the product. A few professional reviews is not the way! Trying to find someone who has similar taste as you and lots of experience can be good. And, on forums, consensus is perhaps the most valuable tool.
I suggest you read the HD800 thread from the beginning going backwards. See how many comments there are about softening them up. And see how many there are about getting more highs.....like NONE! Compare that to your experience.
Do the same for the Stax thread. Then the same for the Koss 950. I think you said you had LCD-2, so read that appreciation thread.
Look for the most common "desires", as in "which amp will bring out the highs", or "which amp will get more bass", or "which amp will warm them up"
Owners do not like to criticize their equipment, so get a clue about what sonic properties they want from their next DAC or cables or amp. When you see something come up over and over and over again, you can bet that it is a general sonic trait of that set of headphone.
Tell me what you conclude. I'll be very curious, and curious about what you end up buying.