I absolutely welcome any chance to talk about writing! My stories are generally frivolous, but I do think about technique a lot, and especially about POV issues.
Anyway, I totally see the problem. And, hmm, I think you could get away with switching scene-to-scene, but only if you were very careful about signalling the change of POV. It would help if all the characters had very distinctive inner voices, and I think you would have to spend the first sentence or two subtly making it clear who was talking now. Perhaps dropping in a bit of description of themselves as a character (something like, I don't know, "as a scientist, I immediately saw that blah blah blah" -- very hard to repeatedly do smoothly, I think) as well as exposition that makes it clear the scene has changed, and maybe even that the previous character could not be in the situation we are in now.
To be honest, it sounds like a headache. I would probably do chapter-by-chapter changes to avoid it. (But then, I also love writing within POV limitations, and especially letting the reader understand more than the POV character does, so I would probably find this sort of restriction fun.)