I listened to the DT880, K701, and AD900 from the same source and I have to say the AD900 was my favorite. This led me to purchase the AD2000 which defined bass to another level for me. Not boomy bass but tight, accurate, extremely fast bass. The best part is that they sound amazing unamped as well. Sorry that I can't really remember how close the ad900 was to the ad2000, its been a long time.
HOWEVER, my friend absolutely despises the ATH-AD series. Yes, some people actually dislike that magical A-T midrange! I think the K701 or DT880 might be safer choices. The ad900 you will love or hate, and at $250 its not a cheap gamble. I never got to listen to the K601 so I can't really say anything about that.
Okay, enough of my ATH fanboyism. I noticed you said you're using a Zero DAC/amp. I use that for my DAC too and I feel like it wasn't properly able to drive the DT880 (They sounded MUCH better on my friends amp/dac). Even my portable amp drives them better. Although you stated that you were going to upgrade your setup in the future, I don't think it will be very fun to not be able to drive the DT880 fully right away. K701 hands down if you're the type that enjoys to analyze music. The detail on the K701 are pretty spectacular for mid-range cans.