I know you don`t want to send the card back under the Rma procedure, but it looks like you are going to have to.
Rather than faffing around with the card, it`s clear somethings is wrong.
A 280X card should never reach the temps you are talking about in windows, at the desktop and while in Idle mode not even playing a game.
As I said it suggests that the cooler is improperly factory fitted in some way to the Gpu on the card it`s self.
It should always sit at about 30c or a bit higher depending on how large your system case is.
And if you also have extra system fans fitted to the case or Chassis.
Just get the card swapped out under the Rma conditions, it is not working to the set default factory conditions most Ati 280x cards do in regards to it`s idle temperatures the gpu core should be.
Take one more good look at the card with the side of your case off, and verify that the fans on the card are spinning when it is hitting the high temperatures you are talking about.
If they are it suggests a badly fitted cooling solution on the card Devin.
The only other thing that would suggest why you are getting a high gpu usage also and high temperatures would be if you were infected with a bitcoin mining program running on your system that you are not aware of.
To test if it is the case, running windows in safe mode would be the indication of such a thing or a bit coin mining program running as a back ground task within windows.
That is all that I can think about as to why the temps of the Gpu and the utilization of the gpu core are so high when the card is supposed to be Idle sat at windows desktop, and not even playing a game ect.