Overlay antipodal map on OpenStreetMaps

I have a page where I overlay various stuff on OpenStreetMap and am looking for someone to add an antipodal overlay (which would mean getting the appropriate tile, flipping it upside down, and overlaying it). My current page:

https://barrycarter.github.io/pages/bclib-tester.html

https://github.com/barrycarter/pages/blob/master/bclib-tester.html