I have read that Shanghai had been promised the world premiere of Soarin' over the World, so we won't see it out here until it has debuted there. I have also read that the on again off again schedule of Soarin' right now is so that testing for SOTW can go on during the times when the ride is closed to the public. I'm guessing the wait for the new film in DCA won't be long after Shanghai
Disneyland opens.
As far as why Soarin' isn't listed as closed on March 23 I can think of two possibilities. Either the website isn't updated yet, or they plan to hold the ride open a little longer during spring break. That week and the week following will be the peak of spring break crowds since those are the weeks surrounding Easter.