Solved!
For anyone who's interested...
My issue turned out to be both the new Arduino Uno and the Solder Flux on the board.
I didn't know flux was that conductive... enough to short out pins on the Arduino. After desoldering every header pin on my Pro Mini and cleaning it thoroughly, I resoldered 6 headers without flux and plugged it all in....
The Uno started giving me signature errors for which I still have not figured out...
I then tried my UsbAsp and after some tinkering with the drivers on my Linux system, I was FINALLY able to successfully load a sketch to my Pro Mini.