There are a number of spoon constructionists who have dropped in and leave useful old threads for your research. Using the way back machine (the search function), Tom left an interesting answer regarding Duhme near the end of this 2007 query: viewtopic.php?f=2&t=6344&hilit=tipped+handle
Trev, Cheryl, Wev, WesternPA and many others post lots of good info. that can be dug up, even if your shovel is only a rusty spoon found in an abandoned dump! You could also look outside at, among others, silver salon forums (SMP) for discussions with simple keywords or strings. Of course, a frontal tip looks more fashionable and tended to render the rear tip as an archaic design. Specific engraving practices, needing a surface for monogramming, might have affected the choice of design along with localized reasons of presentation in settings. What's an acceptable practice in one place might go against the grain in another.
In the case of the Platt firms, I suspect it will take a number of seen samples to tell if they flipped their spoons at a particular point or were carrying both styles concurrent to each other.