But if you voted for any Senate candidate in any other state, it is flat-out illegal to vote in the runoff.
Citation?
I think you just have to live in Georgia and register by December 7. If you moved into Georgia between the November election you can vote in the runoff after voting in your original state.
My fear is all the people who "move" for the election. I expect there will be dozens of new residents at some Atlanta addresses in the next couple of weeks.