iMovie says storage almost full, but it's not.
On my 64 GB iPhone 6 running iOS 8.2, iMovie won't let me create a new project because it thinks "there is almost no space left on this device. You cannot create or edit projects until you free up some space." According to Settings > General > Usage there is actually over 27 GB free. The issue appears to be unique to iMovie. Garageband, for instance, has no trouble letting me create a new project.
What I've already tried:
Restart
Removing derelict apps
Removing all music, photos, videos
Restore from backup
Any thoughts? My inner Fellini is crying to get out.
iPhone 6, iOS 8.2