Sorry to dash your rejoicing, but I just did a search for Branch Rickey in the Sporting Life magazine online archive.
Branch Rickey IS included in the checklists published in these 1907 issues:
March 30th, April 6th, and April 27th.
These are the only dates for ANY year in which Branch Rickey is checklisted , so it appears there was a VERY narrow window to order his cabinet.
To see the checklist for those dates, in the search box for
www.la84foundation.org type:
Phototypes, "Branch Rickey"
The checklist states:
AMERICAN LEAGUE FOR 1907
NEW YORK CLUB
...Branch Rickey