Best bassy yet balanced headphones?

Would have to say the Beyerdynamic DT770 Pro

DT770s are definitely a good choice in the only few excellent closed ones. Their bass is fast and sharp enough, but does not perform so good when it comes down to 100Hz or below. Given your budget there is also T70p worth trying, but I would suspect if you could appreciate their bass since its quantity is much less than DT770. 

Also look out for the D2000. Fantastic bass especially sub bass. Quality/Value ratio is somewhat better than the D5000 if you can get a good deal on it.

Also check out the Denon D1100, really good value especially the price has been lowered during the holiday season. They have really rich and extended bass, more punchy than the DT770.
 

I have similar taste in music to you.  I have in my possession right now: Denon d2k's, srh840s, maudio q40, senn hd-25, AKG K167, HFI-780s, and DT770 Pro 250ohm.  I am running them all through a Fiio E11 and am trying to test them all out through a lot of diff genres and am starting to see my preferences come out more and more.  

FOR ME, I cannot speak for you, but I find I am enjoying the ultrasone hfi-780s the most for the music you specified.  The shure srh840s are a close second.  The hd25s are excellent also, but not nearly as comfortable as the others I have.  On these three cans, I find they have the punchiest, most impactful bass, and your preferences on the other frequencies will determine which is best.  The shures sound more analytical, maybe if you are 60% metal and 40% edm i'd go with those.  If it were the other way around I would get the hfi-780s.  I honestly think the 780s are gonna be the ones i keep after I thin the herd a bit.  It is really difficult to compare them all unless you can actually listen to them, so I really recommend you try as many as you can.