Tested a 360 mp4 file in Videopad 13.59.
A section was excised. Then the project was exported as an mp4 via the HOME toolbar 360 button. (Other formats may also succeed.)
To view in VP, right-click in the preview window... 
The exported clip looked fine in the GoPro player.
Share a sample file or two, just as you did the jpg files above, and someone (perhaps with more extensive knowledge) will check it out.