Todd, I don't know a lot about these premiums, but I think this is an interesting topic. Are you asking if the National Chicle premiums could have been issued in 1934-1936, instead of only 1936?
I checked some of the bios/stats of the Color Tints and Eugene Schott began his career in 1935. I could not find a player that retired before 1935 or changed teams, but I haven't nearly looked at all the players.
The only thing I came up with in a search on the wrappers was this old Trader Speaks article by Bud Tompkins
http://www.sportscollectorsdaily.com...pany-wrappers/