AA agents in SEA will be able to print you a boarding pass. If you're within 24 hours of your flight, you can go to the AA agents at any airport and get your AA boarding pass. You should also be able to check in via the AA app.
FWIW, the contractor operating the shuttle will accept a copy of your itinerary showing an AA flight in lieu of a boarding pass.
If you have PreCheck or AS/AA elite status, it's often quicker to walk outside and reclear security in Terminal 4.