This is gonna sound flippant, but blow a hundred or so on a basic one-light Strobist setup (you already have the most expensive bit--the SB-700; you just need triggers, a lightstand, umbrella and swivel), and
take your SB-700 off-camera.
That's liable to do
far more for your "mostly available-light" portrait photography than switching to a full-frame body will. Especially switching from a current crop sensor 24MP camera to a current 24MP full frame camera. You can't get a higher-resolution camera without going to the D800 series. You're only going to get about a stop better high iso noise performance, and about one stop more DoF control.
Just me, but rent a full frame before contemplating purchasing one. It's one thing to read about all your lenses getting 1.5x shorter and the beauty of full frame. It's another to experience it first hand. Most of us who shoot full frame know that there are differences, but
they're smaller and more subtle than those who haven't shot full frame tend to think it is. And
good off-camera lighting can even make a cheap 1/2.3" format P&S sensor look good.
Just thought I'd put it out there.