I am pretty sure they did one side at a time at DCA. This is not possible at Epcot due to the already massive wait time. Imagine the firestorm of guest complaints that would arise from Soarin' running at best 50% of normal capicity.
Soarin at DCA was closed and done all at once. This was done in conjunction with the re-do of Condor Flats, so that whole area of park was closed.