I'm a fan of the transparent, solid fill shape on top solution and would add that if you use it, make sure to also hide the video from accessibility tools, since without that, someone using keyboard navigation could still tab to the video and hit enter to play/pause it. And if you had wanted to alt tag the video so screen reader users knew it was there, just alt tag the transparent shape instead.
Hiding the video from accessibility tools isn't necessary with Adam's layer solution, as the Prevent users from clicking on the base layer setting also essentially hides everything in the base layer from accessibility tools while that layer is open.