If you stick with ORD, then be aware that getting an alternate (non-AA) flight to SLC might be difficult. BA, I assume, has staff in T3 with AA and maybe someone in T5 arrivals. Maybe. AA have staff in T5 in the luggage recheck area but maybe a skeleton crew and they might not want to touch the ticket if you have a chance to catch your flight.
Delta is in T5 and UA is T1. Everything is accessible by train but it might mean going from T5 to T3 after with your luggage if you're close to catching the flight and then back to T5 if you switch to Delta. T1 (United) is accessible via walkways airside. DFW is also huge with trams but at least all of the terminal transfers are airside whereas the tram at ORD is landside.