Well I may be out of luck:
This thread seems to indicate my current WebGLRenderer based scene will not convert to a scene that uses a CSS3DRender because of depth sorting and perhaps other issues. I saw the idea about “leaving a hole” in the WebGL content and put CSS3D rendered content there, but my videos are displayed on the surfaces of cubes, sometimes rotated, so that won’t work.
So it looks like I have to stick with self-hosting videos. That’s really too bad since it’s a much harder sales pitch to my users. That is, to tell them they have to upload a bunch of videos instead of just dropping in a bunch of YouTube URLs.