I assumed that the records for immigration listed at the archives are Osnabruck, Hannover and Wolfbuttel. I am assuming those are sort of counties or districts that include a buch of towns and villages.
Sort of like St. Louis City is part of St. Louis County, Missouri, USA. The city is the city but the county includes many municipalities, cities, villages and towns.
Of course this is my own assumption and not fact.
I am also thinking that its possiblethat some of the people that got permission out of Hannover possibly may have been born outside those districts but maybe lived there for a time, athough that is assumption on my part an not fact.
P.S. Where did your Schroeder and Meyer family live in the U.S.? I'm thinking its possible that they could have lived among and/or immigrated with people from their home places in Europe. Perhaps there
is a church record of a marriage or baptism here in the U.S. which might perhaps include maiden name of female Schroeder or Meyer that isn't as common a name.