Hi James, what you can do is set the default size for your video host on Settings > Media to a high number, keeping the desired aspect ratio. For example, double or triple both the default height and width values respectively. On very large screens, this will not be full screen but there is always the “[] full screen” button 🙂
On smaller screens, the size will be reduced to fit the screen while respecting the minimum margin (you can set that to a minimum if 20px) to allow for the close button.