I went with the classical 3d plateformer orbit camera with a collider, which is known to be disorienting, especially indoors. This was a contentious point in the team at the beginning of the jam, because we opted for an indoor setting despite knowing we would depend on an orbit cam. This is why btw a few of the corridors have an open roof or very high ceiling. There is a few cramped places, and indeed the camera in those is really bad, I'm sorry.
The classical solution to this is mark some geometry as traversable for the camera, and use one-sided geometry. I actually had implemented such system, (The SEEAG collision group here) it would have been especially useful to mark columns with it. But due to the way the level was designed and time constraint, I didn't have the time to make it work.
Katamari's controls themselves are unique: You use the two sticks of the controller to steer the ball in a direction, as if the left stick and right stick were mapped to the left and right hands of the Prince, the camera is fixed in the direction you are moving toward. It's worth noting that Katamari is a very old game, and was made before any insight on good camera controls existed, and in my opinion the camera is probably the worst part of Katamari. So I doubt that locking camera to character motion would have helped. I opted for the orbit cam with independent directional control because I was expecting most players to use keyboard, so I developed and tested with keyboard, only adding controller support later. Katamari controls were actually planned, if only as a nod to an amazing game and inspiration, but I didn't have enough time to get them in-game.