I've heard Norma Jean and I must say, it's quite awesome. With the bands you've listed, be sure to try This Day Forward by the way. Really great band.
Saosin's awesome too, stumbled upon some MP3s of them some time ago, and I must say, it sound great, no doubt.
Have you heard Walls Of Jericho by the way? Brilliant band with, get this, a female lead vocalist. Not that you can hear it, she sounds as brutal as the next screamin' guy. On top of that, the music's just top-notch.
Mind, you may not like all those bands I've listed, depends on your taste, really. Do try Envy, they're screamo/hardcore/indie from Japan. Madball's New York hardcore, Better Than A Thousand oldschool straight edge, This Day Forward pretty much modern-day brutal emotional hardcore, Run Devil Run's krishnacore, The Dillinger Escape Plan's technical chaotic stuff, Minor Threat's 80s straight edge hardcore, Within Blood's Australian tough guy hardcore, Malkovich's pretty much indie-like up-tempo hardcore from Holland.
Some MP3s:
Walls Of Jericho - There's no I in **** - forking HARDcore
Envy - A cage it falls into - emoscreamoindiecore, forking brilliant
Albert React - Breathe - thursdaycore
Malkovich - 005 - Dutch indiehardcore
Mohinder - The static cult - stressemocore?
This Day Forward - Sunfalls and watershine - modern day hardcore
Waking Kills The Dream - A depth still deepens - kinda screamo
Yaphett Koto - First meetings agreement - yeah baby
Oh, and don't forget At The Drive-In, Poison The Well and Deadtofall. In any case, enjoy.