I don t think you could legally do that, it sounds like you could get the url of a video in youtube and just play it on your web with another player, avoiding apps, youtube logo...
On the techical side the cube strip system is different, and yes somehow you have the equirectangular which could be used with webgl but don t know about the sizes as is intended to be for old little mobile devices.
But yes it would be a nice cheap server for all of us