FYI Latest Soarin' FP time for June 16 - last day of old Soarin - seems to be 6pm. (My flight lands at 5:15pm, so I constantly refresh 2 browsers for later times - nothing, but all times before then are available.)
Also: it's not surprising that the mobile app works and the desktop site doesn't at times of high demand... If I were Disney, and had the choice to prioritize traffic, I'd definitely maintain the service to the mobile app (where oodles of park-goers are about to be in parks using it, and where images sizes they're serving are much smaller...).