BUT: I really don't know what to do with the results???
Not sure it answers to your question, but apparently you did not mention it in the webpage so it might be helpful nonetheless:
sView (http://sview.ru/en/) has a panorama mode which allows to look at the result in a cool way.
The accepted representations are 360° panorama (cylindrical projection), VR180 (equirectangular projection limited to 180°×180°), spherical panorama (equirectangular projection, 360°×180°), and cubemap.
VR headsets probably have similar features, but sView works with a variety of devices.
I just tested with the photo of the "Schwäbisch Haller Globetheaters" on the page you linked and it works well.
I first merged your images in an Over-Under format for convenience (but it can be something else), opened this result in sView [Desktop UI] with the correct input mode selected (Media>Stereoscopic format>Over/Under), and started the panorama view (View>Panorama>Cylinder)
Then I could view it interactively in the output format of my choice, for example in interleaved mode on my 3DTV.
On the mobile UI, it is a bit trickier because the menus are not shown. You can disable the mobile UI in the settings, or check and uncheck the "stick to panorama 360°" option also in the settings, which has the side effect to enable the panorama button in the UI, where you can then choose the cylinder mode.
The "Track orientation" option in the panorama menu make the image follow the orientation of your device so that you can explore it by turning around. It does not work very well with the poorly calibrated sensors on my device, but it is nice feature.
Keep an eye on stereopix.net, because the panorama displays will be added in the future, but I cannot predict when. It is one of the features I want to add to its viewer. I am quite impatient to be able to finish the first part because there are several subjects discussed lately that can be added to it after the big change is ready.