Having been through this same question lately, I have found it hard to find the right headphone from other people's reviews. All our ears and hearing are different and technical graphs are only useful for a comparison from one phone to another but even then so much else is subjective. I did find the 107 portable head phone shoot out here very useful. Probably ljokeri has written some of the best comparisons in an layman's language you'll find. It certainly helped me short list.
That said, I purchased a set of DT1350s which I found I can only use at home in a quiet environment. While others seem to get good isolation and you might too, I don't and therefore they just won't do in even moderately noisy environments. I have the suede pads on the way and hope they seal better because I do like the overall sound of these when I can get them to seal which they do seem to do as the pads warm up and get more supple. This however is totally unsuited to travel and casual use.
I purchased a set of Amperiors and I think these are well worth you trying. They have nice detail and stronger bass than the Beyers but not as detailed IMO. But I found the mid bass hump a little too much for quiet listening. Unfortunately I did not try them in noisy environs before returning them. I just knew over time I would rarely listen to them. Still I would like to try the HD25-1 as a comparo. I auditioned a set of Momentums when I returned the Amperiors, end these are much more comfortable but to my listening not suitable either.
What I did try and like for travel is a set of B&W P5s. Before everyone asks why??, let me say they are not perfect but in a plane and for casual listening, I quite like them because they are comfortable for long flights, compact to pack into my travel bag, easy to put on or off or hang around my neck when the steward/ess talks to me, do a reasonable job of isolation (but not up to QC15 standards but don't require batteries and are on ear compacts and much better sounding than QC3). And finally, they are not too different sounding than my W4Rs which are my favorite IEMs with the DX100 and I note you have these. I also find them pretty good with classical music. The slightly warm signature delivers lush strings. Of course EQ can adjust most phones but I prefer neutral or near neutral phones, but in some places you just have to have a bit more warmth which seems to be why Golden Ears target frequencies for IEMs have a slightly elevated DB for bass.
I don't have HD800s and not heard them unfortunately and I couldn't risk them in public if I had them, but feel based on your budget, the Amperiors or P5s worth a listen to or if you are near an Apple store, you can purchase and return within 14 days if you don't like them. The ability to do that is worth the slight price premium in my view.
Just some rambling thoughts from a not too technical novice.