So I managed to get the elusive achievement.
As you will notice in this screenshot, my ally Russia, who founded the Eastern Orthodox Church and picked up Wats as a building, is down to only one city remaining. No worries, I build three cities on an island and managed to get the religion spread to them despite France spreading the Catholic faith to all of my cities on my main continent. Once I finished the Holy Site, I bought the required buildings and faith purchased two Apostles. Yes, they spread Eastern Orthodoxy as they should.
Here is a screenshot of Angkor Wat just before spreading Eastern Orthodoxy to the city and purchasing the Wat.
And then I finally use the great prophet who has been sleeping all these centuries to found the religion of the great Moo in the modern era!
One thing I discovered when doing this which I did not know before. Every city which had a holy site built converted to my new religion of Moo instantly! Had I known this, I probably would have built more holy sites.
As for the natural wonder, the first one I found was to the north of Australia. Once I defeated Australia I found the Giant Causeway. I suppose if I had built some navy units early to explore the coasts, this would have been revealed in time for the Inspiration.