After landing we discovered that checking in at the right time might get us further ahead in the line but we tried that, checking in within minutes of checkin opening and were still pretty far back in the lines.
We ended up buying an "upgrade" to get us ahead in the line and next to each other. For us to do that for both flights, we'd have been paying ~50% extra for a feature that comes by default with all other airlines.
Also, while interacting with Southwest's famously "better", more "caring" staff, we were met with total disinterest and absolutely no sympathy.