The only issue I keep having is GSX selects the wrong catering livery (i.e. I'm in American Airlines A320 livery, but it auto-selects Southwest Airlines catering).
The airline you are flying doesn't count for ANYTHING in GSX. It doesn't count for the handling operator, and it doesn't count for the catering operator as well. The manual even has a dedicated chapter about this, aptly named
The Airline YOU are flying doesn’t matter, explaining why. Basically, it would be very wrong if your personal fleet of ground services could follow you everywhere in the world.
Operators (Handling and Catering) are based ONLY on the airport.
If you read the whole chapter about the operator scoring system, Page 95, it explains how DEFAULT operator rules work, how operators are assigned, how you can change the default rules. And, of course, if you don't want to understand those, with an airport profile, you can assign specific operators to any gate, and those will completely override the default scoring rules.
So, maybe, if you ARE using an airport profile, whoever made it has decided that only Southwest should be available there because, when no profile is in use, the default scoring rules at KOAK should have presented you with a menu with 3 different Southwest variations AND Allegiant Catering.
Of course, changing the operator is extremely easy in the Operators tab of the parking customization page, if you don't agree with the choices made by whoever made the profile.