There's only one terminal in Seattle. IIRC, UA's baggage claim area is in the north end of the terminal (on the bottom floor as with everyone else) while BR's check-in is at the south end (on the top floor again, like everyone else). The walk between the se two is no longer than 10 minutes even if you walk slow and take a long time using the elevator (you can use escalators but there are 2 and you have lots of bags).

I doubt BR's check-in counter will be open much before 11p or more likely not until 12a. Call them and ask.