Re: Bieri's of Switzerland then Missouri
I( have checked the Beery books in my possession (Wenger 1911, Garber 1957, Fulk 1976) and do not find a reference to a Beery or Bieri who might be the Lewis/Louis born about 1726 for whom you are searching.
In my study of the Swiss Bieri/Beery family, I do not believe I have ever found any who changed their name to Barry or Berry.
There may have been a brother of Nicholas Bieri, William?who went south rather than to Virginia, Ohio and the midwest as did the Nicholas descendents. Perhaps Louis could have been of that part of the family.
Several libraries have copies of a book listing imigrants from the German Palatinate in the early 1700s. They were required to sign a declaration of loyalty to the governor of Pennsylvania. That might be a source worth checking.