I’ve had mostly good experiences checking in at AUS. The only real problem is that they can be overwhelmed with the hordes of travelers, and I’m always cutting it as close as possible w.r.t. check-in times. In this case, if you hvae status, I’d try to arrive about 2 hours prior to departure in case there’s a line or the agent has trouble. Without status, I’d add at least 30 minutes more. It sounds like you’re aiming for an evening departure, and the check-in desk isn’t usually as busy then as it is in the mornings. The last time I flew on a split ticket from AUS was May of last year, and it was straightforward, but there’s always a chance you’ll get a brand new agent.

As far as what to say: “I have a connecting flight from SFO on a separate ticket; can you check my bag through?” Hand the agent a printout of your itinerary, including the fare classes and ticket number, if possible. That should be it. If the agent starts to argue, you can pull up the appropriate UA policy and say something like “I had a friend who had to do this, and he told me the agent had to call their help desk, if that helps.” The help desk really shouldn’t have to get involved on a UA->*A transfer, but they should be able to tell a recalcitrant agent what to do regardless.

BTW, while you may only be seeing a couple of connecting flights to SFO when you’re searching for award flights, AUS-SFO has a lot of lift; depending upon your day of travel, there are 3-5 nonstop flights plus probably 10 more connecting itineraries you could take (through LAX / DEN / IAH). So if your flight looks like it might be delayed, don’t hesitate to get to the airport early and plead your case.

PS: Southwest would not be able to check your bags through to AI. They don’t check bags through to anyone. So they’re not a great option.