I just did exactly that upgrade.
I went from HD 555 to AH-D2000.
Your tastes seem very similar to mine, I like a little bump in the bass for emotional power, nothing boomy. The highs are pretty similar to the HD 555, maybe a little higher, nothing too much. I also like classic rock, easy rock, ambient and alternative, like you. These are probably the headphones for you man. The bass is not boomy, trust me, it's just right for rock and alt.
I know what you think you're missing with the HD 555. I mean the clarity is there, the mids are there, it's just so damn THIN!
You can't really go too wrong. I like my new AH-D2000 allot. Tons of fun.
One thing to add -I've tried the Hd 650 too. Highs are less vs HD 555, I think. They seem made for acoustic to me, they do that damn well. I'm not sure though, I'm a noob. I ended up grabbing Denons in the end, they suited my music better.
I think the whole "other class" thing is overrated, I doubt allot of these guys saying it can abx flac vs. mp3. It's this obsession with spending tons of money I swear. The clarity is very similar between the two. The Denon might seem to come out with less because it has more bass, but it's all there.
Have you heard the Denon before ruling them out? I think you're instincts might be right if they are the same price. I got mine for about 272$US total, here in Canada. The Hd650 would have costed me about 384$US.
You can't go wrong with either. Get your headphones already.