You should note that you are not able to use RAC earlier than 12 hours before your flight (and the hours are 5-1, so you can't do it even that far in advance if your flight time is before 5:00 p.m.). If getting those business class seats will require that you do it sooner than than 12 hours, you may need to find a plan B to get it done at 24 hours. I'm also not certain that the RAC desks even are set up to process upgrades for you.
My suggestion would be to have the front desk at your resort or one of the guest relations locations in the parks or at DTD do the check in/upgrade for you at 24 hours. They will do SWA check ins for guests, so I don't know why they wouldn't do this for you. Another alternative would be to have a reliable (100 percent) friend or relative do the check in for you from their computer at home. You'd just need to provide them the information they would need to log on and do it.