To address your concerns specifically:
-There's a limit on how much depth any headphone's soundstage is going to give you, since the two stereo channels are isolated and cannot interact the way they do with speakers. However, if you feel that the DT880 is deficient in this regard even in comparison to other headphones you've heard, then that's different. I'm not sure there's anything you can do to fundamentally alter the presentation of any headphone, though of course there are those who feel that different amps and DACs can have at least some effect here.
-The harshness you hear is intrinsic to the tuning of the headphone and is chiefly caused by a spike in the 5-6 kHz region. This is the main flaw in the DT880's tuning, IMO, and can only be truly eliminated by using EQ. Amp and DAC selection isn't going to remove a narrow, high-Q spike like that, though it might have a broad effect on the overall balance of the headphone that helps mask the effects of this spike.
-Imaging is a little puzzling, since I've always been quite impressed with the DT880's ability here, save for a very slight difficulty they seem to have in creating a center image. The only thing I can think of is that your particular pair has poor driver matching in the upper end. Good imaging requires well-matched, smoothly extended treble, or else positional cues get smeared and imaging suffers.
-As far as the recessed mids, I think it all comes down to personal preference. I've never felt the mids were deficient, and I highly doubt our DT880s are fundamentally different in this regard, so we're listening to the same headphone essentially and drawing different conclusions. This is a normal part of the hobby, and I'm not going to tell you that you're wrong. Rather, I think it's possible you might prefer a different balance, with more forward midrange and a bit less treble than the DT880 provides. You might want to look at something like the Sennheiser HD600.