AA doesn't short check either.
With a 2:20 connection and the need to allow at least 60 minutes waiting for the bag, this does not leave OP a great deal of time as he must deplane, make it to Flight Connections, wait at Flight Connections, walk to baggage pickup, do whatever it is that he plans to do with the bag, and then head back out to his IST gate. If the bag takes 60 minutes, that is 1:20 less conformance and any other minor delays.