I have pulled a temporary fix from an old thread. While it does work, it's a royal pain and requires a bit of back and forth to get it to work.
http://www.swtor.com/community/showthread.php?t=904310
Just paste C:\users\[username]\AppData\Local\SWTOR\swtor\settings into your search bar. Go to that folder and open up the "client_settings" file. You don't need to delete it like the above thread says. Instead, plug in the desired resolution under "height" and "width." I think what this does is lock the resolution at that level. When you boot up you'll still be stuck on 800x600 and still unable to access the drop down menu. Hit Alt+Enter to go into windowed mode. It'll grey out the box entirely. On the left, switch it manually back (using the drop down box) to full screen and it should pop straight into whatever resolution you plugged into the "client_settings" file. It's worked every time for me so far. But it's a real pain since you have to do this every time you launch the game.
I'm 95% certain it's the patch at this point.