Kevin,
Not sure why you are getting a black box.
That said, I tried a few methods to get the best possible shot of my character.
Right now there are two models used in game a high-resolution model/texture in cut scenes for detail (because what is drawn can be controlled), and a lower resolution one for general game play.
I personally believe (thought I could be wrong) the character select screen uses the high-resolution versions and provide a good framing for a bust shot. If you have Picasa (if you don't, you can get it free at picasa.google.com), simply open up Picasa then alt-tab back to SW:TOR. When you hit "Print Screen" Picasa will generate its own screenshot (SW:TOR does not recognize the Print Screen button at the character select screen).
Because of the looping animation, you should find a few "poses" that convey the right 'look' you want your character to have. As that pose approaches spam the Print Screen key a few times. This will give you a good selection of images to narrow down to the one you like best.
Once you have that, anyone with intermediate skill in Photoshop should be able to remove the background around your character.
Well... that's what I wound up doing anyway and am quite pleased with the character shot I was able to get using this method.