I thought I would share part of an email from our relation in Germany. She wrote:
The name "Menge" may be the Diminutiv of "Mann". In dialect folk may call "menge" a little Mann. In plattdütsch it is "Männke", in Hochdeutsch it is "Männchen". In Bacharach/Rhein my forefathers in church records were written "Männge", so you can see they were thinking of "Männchen".
What is wonderful about this explanation is that in the old Philadelphia church records, we did find occurrences of the spelling "Männchen" or other spellings very close to this. Especially since this spelling varies significantly from "Menge", I always felt somewhat nervous about whether the records we found really do apply to our family. Now those doubts are gone. Amen.