I played with the Quake engine back in 2011 to experiment with how to use and configure a panorama in a game with Lua scripts. You can build your own camera cubes/prisms and use different lenses: http://shaunew.github.com/blinky/)
One of the results of my experiment is that the equirectangular projection is, well, fucking horrible for anything wider than 90 degrees. Lucid.it is a great tool, but no panorama tool should only allow the equirectangular projection. When you zoom out, you notice that the periphery becomes stretched, almost inducing nausea. There are better projections, namely the stereographic ones. You can see an example here of a 180 degree view of a panorama: http://www.ashnu.com/stereo.htm
I would like to get your panorama video working on a stereographic projection. That may require using a different tool or building one.
Also, did you explore the "philopod pitch variation" you mentioned in your first post for just using four cameras instead of six?
4 cameras wouldn't work very well with the cameras I used. It was a struggle with 6 cameras to find enough overlap get good quality stitching.
One thing that would be great is to get cameras that can be arranged in a tight enough configuration that they all share the same non-parallax point. Then, you don't have to do anything fancy to stitch them.
One piece I kind of glossed over is that at lower altitudes the ground is much closer to the camera than the sky. That means that you can't create a general case stitch profile as you're not working from the center of a sphere (in relation to the objects you're trying to use for control points), so as the payload rotates you have to stitch each frame individually. I may play at it some more and try to get a stitched video of the low altitudes of the descent. First, though, I'm going to take a break from the project for a bit.