Ha! Well you could try deactivating CS6 yourself on the other machine so you don't have to keep turning it off. Do that through Help>Deactivate.
Just to let you know though, I did get Adobe to deactivate my machines when this happened to me (my fault, not properly keeping track of which of several cloud licenses were installed on which of several training computers i use) and it was fairly painless. I used the chat window instead of calling them. Once everything was reset, I reactivated and better managed my licenses and all is muuuuch better in my world.
Michael Riordan