If we're playing the least dangerous choice game (not that I've ever liked this way of choosing), HD600 couldn't possibly offend and it's very good. I've noticed several on FS at your desired price. Between the other two, K70x has better soundstage and DT880 is more comfortable.
HD600 and HD650 are very similar in most ways, HD650 are just slightly more refined and slightly darker sounding than HD600. Many will consider them as musical which means you can enjoy the music without being distracted by the highs(no harshness). They are as detailed as DT880 and Q701 IMO, just in a way that the highs are not exaggerated and not giving you a false sense of detail and you can discover much more bass and mid information much more easily as they are less bright.
I have tried many headphones (AKG K712,Q701,K812, Beyer DT880,T1, Senn HD800) and I find HD650s are the most enjoyable and smooth right out of box without EQ, amp ungrade and spend a lot of money smooth out treble harshness. They can sound good even with iPhone. They are not amp or source picky and can scale very high with better amp and source.
If you are concerned about listening fatigue then HD600 or HD650 are the most safe one.
If you like wide sound stage and brightness and don't care about the bumps on AKGs, then Q701 is very good.
If you don't mind narrower sound stage(which is good for certain music) and want a good all rounder, DT880 is the one. BTW DT880 is slightly less bright than Q701 from my impression.
DT880 can be so engaging and have no harshness when properly EQed down the treble peak (haven't buy and tried that with Q701, I just hate their headband bumps).
From measurement data, DT880 250ohm and 600ohm doesn't have a big difference but the 600ohm one are indeed more refined and most people refer to the 600Ohm one as more balanced(less treble). If you choose DT880 then choose the 600ohm one because O2 and ODAC can properly driven them and you have better SQ.
My personal ranking:
Treble Smoothness: HD600/650 > DT880 > Q701
Treble clarity: DT880 > Q701 (did not include Senns because its hard to justify with less treble presents)
Wearing comfort: DT880 > HD600/650 > Q701
Sound stage: Q701 > HD600/650 > DT880
Bass quality: DT880 > HD600/650 > Q701
Bass quatity: HD600/650 > DT880 > Q701
Sound Richness and Musicality(make you forget you are wearing headphones): HD600/650 > DT880 > Q701
Thanks for the detailed response. What do you mean by treble smoothness and clarity?
I won't be able to get the 600 ohm version of the DT800. Too expensive.