Origins has quite a few issues with more than 4 players that have to be addressed by a mod. it is completable on my servers, for example, but not exactly in the vanilla way. you have issues like challenge rewards not working correctly, so not everyone can get fists (which is required for ee), crashes that have to be addressed by a mod, etc.
i don't believe there is a public mod to fix the easter eggs with more than 4 people on these maps, but some servers have fixed them or at least made them completable in some way.