SWA is a major sponser at SEA WORLD, I think that may have something to do with them not being a participating airline.
But, that really is no big deal. You can check in at any Disney resort or guest services at the parks 24 hours in advance of your flight. You only need to bring your bags to the pickup point at the resort and only need to handle your bags at the airport. That really is not a lot for a free ride and inbound service.
SWA does not accept emails. You would have to use snail mail.