Dan,
Home Run cigarettes are rumored to have begun around the 1890s or early 1900s and the brand was made into the 1960s (at least, and possibly to the 1980s). I've never seen anything (i.e., a pack or flattened wrapper) that dated the brand to the 1890s or early 1900s other than the purported advertisement pieces as well as a newspaper article that Carlton has. However, Jim Shaw, a very experienced cigarette collector, has a pack dating to 1918 which is pictured on his website here:
http://users.ap.net/~burntofferings/...gett_duke.html. In addition, I have a wrapper dated to 1925, which I can scan and post when I return home after the holiday weekend.
With respect to the carton I have, you are correct that those packs date to the 1960s era.