my vote would be "1920's" or just "1920"
there are other "portrait" cards (see the box display pics ) Cobb, Johnson, Alexander, Bancroft? (Giants)
whoever that NY Giants player is, is going to be the KEY in dating it IMO 
also you missed one player in the "portrait" type, the bottom right player in the image with tape on the toploader (images was in one of the old threads).. someone said Thorpe? (unlikely) and someone said Toporser w/o his glasses? (very unlikely, average player started in 1921)
you must consider the other "action photo" type too, since the only known complete box contained them as well (Boxers), and someone pointed out the boxers are more likely from the early 20's.
the baseball player "action" cards are not going to be easy to date....
but looking at stats is unlikely Hornsby would make this set if it were made before 1920... (Ruth "batting", Sisler , Coveleski prob wouldnt made the set if issued before 1919)
quick list of Players seen on the "action" type are ...
Alexander (same pose as E121)
Hornsby
Ruth
Sisler (same pose as E121)
Coveleski
Johnson (same pose as E121)
and the 4 boxers
the boxers should date it better
and also the other stuff in box might help ie actress images etc.
another interesting thing is the image on front of box shows strip cards in a strip, these were more commonly sold post1919
love this stuff
very interesting!