It's REALLY hard to say just because I haven't heard the 2400's. From some initial research (ha! gold-plated drivers!), it looks like the 780's are going to be closer to your cup of tea. You'd probably want the 580's only if you really wanted extra bass than either of the others, and honestly, that's something you're not going to be lacking with any of these headphones. And I will also say that the extra clarity won't help you at all out of an inferior source; my old Alienware-branded HFI-700's would crackle on piano notes coming straight out of my laptop. If you're doing computer listening, I would definitely recommend some kind of cheap external DAC/amp (I use the FiiO e17 currently and it works fine, and I have an Aune T1 currently en route from China).
Soundstage won't be as wide, though, simply because it's a closed headphone. It's certainly VERY good for a closed headphone. I personally enjoy the extra isolation in a house full of people, and that's a much greater benefit for me since I can actually hear the music. It would be very understandable if your preference were different depending on the situation.
The HFI-2400's actually look very nice, I'm a little surprised I haven't heard more about them. 780's are going to be an extremely similar sound quality, and for your rather specific wants I think they might be the better choice.
EDIT: If you do go with the 780's, try to wait a little for Amazon's price to drop back down or for B&H to get them back in stock. I think Amazon only went back up because B&H ran out.
EDIT 1.1: I'm going to send you a PM...