+1 on the DT880. It's prolly the closest you are going to get that I have heard to both worlds. I am also considering picking up a pair of AKG550's that are closed (the 880 is semi-closed) and they sound like they might fit your needs.
Read what Tyll says about them here:
http://www.innerfidelity.com/content/wonderfully-competent-akg-k550-sealed-headphone
There is also a video he does on page 2 of that article. In terms of recording just listen to what he has to say about the high end (you can't have everything).
Lastly in regards to the 380 yes you can get a 3.5mm to 2.5mm cable to replace the coiled. Some cables need a little shaving around the plug. I used the Sennheiser hd210 replacement straight cable which required no modification here: http://www.bhphotovideo.com/c/product/547683-REG/Sennheiser_091581_Replacement_Cable_for_HD.html
Yes the 380s are not the best choice for most music listening. If you want something that is "fun" I love my Beyerdynamic DT990's. They are an open can and I would think they would be good for gaming due to the sparkly detailed high end (I know it's weird but I'm not really a gamer so just from what I hear
). They have a lot of bass quantity for an open can and good extension and quality.
So you could go: DT990 + HD380 = $350dollars for two different uses
Or -- DT880 for all-rounder -- $250 to $300
Or -- AKG550 for all-rounder -- $300.
You will need an amp for the DT models for best sound.