Someone sent me a pamphlet composed by David L. Shreiner, who has traced Hans Adam back to Gommersheim, Germany. I can e-mail a PDF if you'll send me a message DNACousins@aol.com.
I am the administrator of the Schreiner DNA project at Family Tree DNA. There appear to be two separate DNA signatures for people who believe they trace back to Hans Adam, so we have a mystery on our hand. So far, the participants all go back to Pennsylvania, but any male with the surname Schreiner is welcome to join the project: