An interesting thread! If I just could throw in my two cents here:
1) I think, the entire discussion about what's better - speakers or headphones - has too many parameters to consider to be universally relevant. They are just very different. Headphones are just as capable as speakers to convey spatial cues, the problem is in recordings - the vast majority is made and optimized for speakers. I can spend hours discussing the technicalities of sound perception by a human being and the implications of speakers, headphones and earphones as a medium - but I won't bore the audience. Try some really good binaural recordings for headphones, and you'll be blown by how realistic the soundstage can be in heaphone listening :-) Dr. Chesky's recordings are a good example.
2) I think the area where you will get most improvement for least money will be... your music collection, or, more precisely, the storage format. At zero cost you can have some audible improvement, especially in micro-detail and overall ambiance. Some may argue that a 320kbps MP3 is undistinguishable from the original red-book recording in double-blind test, especially if the rig is not ultra-high-end. I would agree, that this could be the case if one just listens to the music. But here we have a different story: clyw is really hunting for performance, details and nuances. clyw, make a simple test: try just one of your favorite discs: burn it into a good FLAC, and do some comparative listening: you may well hear the difference. Even if you don't - you risk no money, just a couple of hours of your time :-)
3) When you try the above (i.e. try binaural recordings to see if you get good spacial impressions from specially made recordings and try uncompressed audio to see if you hear improvement in micro-detail), based on your findings, you may carefully move forward with gear adjustment, if needed. I have no personal experience with Schiit, so can't comment on this, but as for your current cans - I am certainly not in the Grado's camp - this is just not my sound. BDs are a closer match for my taste, and are generally quite capable cans, but at 250 Ohms they need a decent amplification - although, at least on paper, the Magni should have enought juice for them.
4) If you can - find hi-res samples of your favourite music to use full potential of Modi's 24/96 playback. If the improvement is audible even in blind tests (foobar has a nice tiny plug-in to facilitate the testing process) - maybe the Mody simply shines better with 24/96 than with Red Book...
Hope it helps!