Based on those songs, I'd say... the Denon D2000 may be a poor fit. Especially with In Too Deep and Higher Ground. It just vibrates too much.
ATH-M50 is also a no go.
And I wouldn't go for V-Moda M80, since it sounds a bit too boomy with Burnt Out Car. If the M100 is any similar to the M80, then I would say those are out as well.
It's funny since this seems like it would be an easy request. But since you ruled out DT880, DT990, and HD600, which more or less are known for good speed under the $300 range, it's... actually quite hard to find something that surpasses those headphones in speed.
I have heard the HE-400, though, and I can pretty much agree with what has been said here. It has awesome speed, transparency, and will probably fit your needs well if you can stretch your budget past the $300 price range.
Alternatively, if you haven't heard the DT880 600 Ohm yet, then I think it's worth a shot. Treble on the DT880 600 Ohm is smoother and less glaring than the 250 Ohm and 32 Ohm versions in my opinions. Plus it has very good bass quality and texture.