I haven't had to do this in awhile since I am Plat now with a 100 percent upgrade rate but when I was a Silver/Gold and had not been updated, I would go to the online check-in once an hour and let it ask me if I wanted and upgrade. Sometimes an R seat would open up and I would get it. Typically this happened more on the day of departure as people used FlyNow (or other methods) to change their flights.