In case it's of interest to anyone ... I've got as far as creating a branch of Ignacio's plugin, and updated so that the user can decide if they want a mobile fallback image. If they do, the image selected as a poster frame will be used.

https://github.com/darloboy101/adapt-backgroundVideo/tree/develop

In a modified theme, I've then created a class that applies display: none to the page header, and positions the background video block I've created to the top of the page.

Yet to comprehensively test.