A fellow board member here acquired this 1910 Philadelphia Athletics Japanese postcard which has the same look and same back as the McGraw and White.
1910 As.png.jpg
The image is the same as the M101-2 of the A's. It raises the question of what the Japanese set really is. It has been long assumed it was a McGraw stand alone card for the World Tour, but I'm guessing it is more likely a Japanese version of the M101-2 with the McGraw issued again during the World Tour which would account for more of them. White was winding down his career by the time of the World Tour and he would been more likely to be in a set a few years earlier? I wonder which other player postcards from this set might exist.
Any other theories out there?