Not sure what happened with SkyWest, but it might help to show them the documentation that has your 2 companies linked and definitely tell your j/s "coordinator", whoever is responsible for the list.
I'm thinking you won't have too many problems with Southwest. They are very good about helping out and getting you on. They only thing about them that I can think of you took care of already- is make sure you list with, who is it? Claire? (the phone bot) because the agents at the airport either can't or just won't list you themselves. I've never asked for a specific reason simply because they've basically always been very encouraging for me to get on.
1. Be polite
2. Be prepared (have your id, CASS code, be dressed right, etc...)
3. Be helpful (you're a crewmember, not a gate agent, but their job is very hard and anything you can do to help out will get you on their soft side. it helps to have bag tags to give to pax, just standing there in line for that very thing, but that's just me)
4. Reciprocate (not just for the crewmembers. the gate agents get NOTHING out of this but you're taking up their time so reciprocate doesn't always have to be for the crewmembers. you can always have a treat for the agents who you are counting on to get you home)
Once you're on the plane:
1. Be polite
2. Be prepared
3. Be brief (introduce yourself. have your id clearly visible. they're supposed to ask for it, but they might not. if you have seat in the back, mention that and thank them anyway and then get out of their face, unless they want to chat.
4. Be a ghost. Try not to be visible in a negative way unless it's crossing seat belts after the flight or whatnot.
I realize a lot of this may seem like obvious stuff, but I've noticed enough bad jumpseat etiquette to bring it up when people ask. Personally, I take notes on each carrier because there are way too many details for my simple mind to hang on to.
