Actually, if you like the HD380 the most, I don't know how much you'd like the D600. From what I remember about the HD380, they don't exactly sound comparable; the D600 will most likely have too much bass for you. I'm actually kind of perplexed by your choice in the HD380. I thought they sounded a bit on the bright side and I don't remember them having much bass.
But if I can make a prediction, you won't like the Grados at all.
If I may make a suggestion, I've been mostly content (The only reason I say mostly is because I want something a little more portable at the moment) with my ZMF T50RP for the past three months. The bass version (V2) seems to be what you want, but I can't promise depth. Here's a link to the website:
http://www.zmfheadphones.com/