First off, do you have a playground with this mesh available ? It would help others help you a lot.
If your recurve wall is also curved vertically (ie like a sphere that had the top and the bottom cut off), then I think you might just use a sphere map the way I showed in the playground before.
In this version I created a cieling and a ground to do this “cut off” artificially (this wouldn’t work though if you need a transparent background on your canvas)
Then there’s the matter of the 360° vidéo. As I said, you can’t assign a video as texture to a material. Babylon is using WebGL and while you can animate meshes, sprites, cameras and particles, it won’t allow animated textures.
Having said that, maybe you could try something out, but it’s a long shot. If your video is not too long, you could try to extract the 360 frames. Then use a custom Interval function to apply the correct frame on each 1/24 seconde (or 1/30 second, according to your FPS).
If you accept a long loading time, necessary to the numerous textures, applying them dynamically should be fast. But I don’t know if it’s realistic.
Interestingly enough, this way of animating a video frame by frame is also used by Apple for its scroll effects (although not in a babylon environment), as done on this page and explained here.