The first mission could be a story hub world, searching for certain areas which would trigger a mission. From there, the game would randomly select the mission after the mission you triggered, so your campaign could be:
Exploration
Citadel
Crashed
All alone
Fourteenth platoon
-----------------------------Canon kicks in, missions are ordered
Reunited
Checkpoint Charlie
Shortout
The Flood
Forward unto Dawn
Epilogue
While your friends is:
Exploration
All alone
Fourteenth Platoon
Crashed
Citadel
—
Reunited
Checkpoint Charlie
Shortout
The Flood
Forward unto Dawn
Epilogue
ODST for me was the best narratively framed Halo game. But it worked because you were jumping back and forth between the Squad, which you won’t get in Halo 4. For it to work like you suggested you would need a MASSIVE hub world, way beyond what ODST had; you’d need something akin to an RPG-size map.
Linear will work for me, as long as the story is deep enough.