I've been kicking around the idea of the possibility of rigging two Go Pro 3 Black's with a small custom mirror rig. The mirror rig would be the same as a 3D rig but I would align the cameras to overlap with no IO or convergence.

With the two cameras connected with a sync cable one should be able to shoot in the 4K 12fps mode and net 24fps.

To the best of my knowledge the only thing that prevents this is the sync cable only syncs the shutters to fire together at the same time. I am hoping that the authors of the firmware would write a feature into the sync mode to alternate the shutter firing. One could then link the two files on the timeline and alternate them in post.

Any reason why this wouldn't work?

How would you mesh the two clips together?

Well that's the question that I'm not sure how to answer yet. Assuming the 3D sync cable syncs the two cameras so that they record synchronized frames, it stands to reason that they should be able to program it to make the cameras record frames that will alternate in their timing. If that's possible, one should be able to line up the two cameras with a small mirror rig and accomplish 4K at 24fps. I would have no problem building a small light weight mirror rig so that's the easy part.

That should be pretty easy if you can get the native footage from both cameras a frame off from each other.
Then you just take the footage into Adobe After Effects and put each on its own layer and combine the two.

Yes that was what I thought should be possible. I have an email in to Tech support to see if they think they can set up the cameras so they will alternate frames between the two.