Hmm. Yeah I was afraid you'd say that. Based on what I have searched so far, I haven't seen a post with headphones that can do all that with my budget. I am willing to increase my budget to about $300 though. I'll look into the other headphones you mentioned.
If I could buy any headphone from $0-$350, what would you recommend then? I may just save up some more.
Ultrasone Pro 750 (closed) if you like a bright sounding can.
Denon AH D-2000 (closed & probably in new open box) if you like a darker sound.
The Ultrasone wins on sound stage and the Denon on bass & sub-bass (the Ultrasone is good--just not as good concerning bass).
To get the bass you want in an open can, the Beyer DT 880 Pro might work for you. If not, the way over your budget Senn HD 650 and HiFiMan HE500 would probably be the next steps up the ladder.