[FFmpeg-user] command line help for merging two 360 streams

[Rudy Moore]

tldr: I'd like to swap half of a video image from a first stream with an equal half of a video image from a second stream. I'd like to preserve the audio on each stream. Suggestions for how to do this with ffmpeg?
I've got two Samsung Gear 360 (2016) and would like to make stereo stitched output from the two cameras.
Each camera produces an MP4 video that is 3840x1920. Those videos have the output of two lenses mashed up against each other. Each separate lens is showing a circular image of about 190 degrees or so. And each half-image is 1920x1920.
I normally use a program called "ActionDirector" to stitch these into a 360 image format. And in the end, I still will.
The normal process is to stitch the two films, then open Premier Pro. I import them both into a project, align them based on the sound of snapping my fingers in the audio. Then I composite them one on the top of the image and one on the bottom. A 3D player can then play this back giving the left image to one eye and the right image to the other.
The problem is that the camera placement is correct when looking one direction (left eye = left camera). But flip it around and now it's backwards (left eye = right camera). So I need to swap that 1920x1920 square from one video stream into the other and vice versa, ideally with no encoding loss.
Suggestions on how to do that?
For a quick hat trick, how about doing the steps that I'm currently doing on premier pro? That is, after the sitching in ActionDirector, how could I merge the two videos into a 360 video, complete with aligning the start times of the videos?
Thanks for your suggestions!!
Rudy