I gave the trusty old New York Times Archives a once over for the period of March 15 to April 15, 1913 and gleaned the following (all dates are of publication and not necessarily the date of the event, more likely the preceding day):
March 22 - break camp at Marlin Springs
-swing through Houston, Beaumont, New Orleans, Mobile
April 1- @ Birmingham
April 2- @ Marysville College at Knoxville
April 4- @ Norfolk
April 5- @ Richmond
April 6&7- @ Baltimore O's
April 8- @ Washington
April 10- @ Yale
Opened season at Polo Grounds vs Braves on April 10
Also did a search for "Thorpe Giants". He appeared to be injured part of the spring and was at some point relegated to the second team (Colts or Yannigans). There were no hits from March 25 to April 9. Make of this what you will.
Once in a while I get green with envy at another's pick-ups. This is one of those times. A most awesome photograph!
