I would pick walking landside (TBIT is uncrowded during the day though you are just walking by it, and it is a 5 minute walk). There is an airside transfer bus for American Eagle (which uses a remote terminal by the hangars), and there is another bus that runs from there to T3. But that would take much longer than walking and clearing security again, also often they check for an Eagle boarding pass before allowing you to use the bus. AA and AS are not able to issue BPs on each other. Other than FF tie-in, there really is no commonality in their codeshares on each other. The only good news is that security at T3 is generally fast, as T3 has a strange mix of airlines with few flights (however they all leave at the same time, so for an hour a day it is bad, hopefully not the hour that you are there).