My 3rd Great Grandfather Adam Kuntz (1813-1878) presented me with much the same problem. One thing I've learned in the last month is that Alsace-Lorraine were two separate places at the time of his birth...understanding the when and how Alsace was at one point Germany and another point France, is helpful to a point, but even knowing when and the how, if you don't know exactly the where he was born, getting the information can be extremely difficult if not impossible. I haven't been so lucky, but if you can get a copy of his immigration records that might have more information than you are currently finding. If someone could advise us both on how to obtain those, we might get further.
As to what the FAG Memorial has, they are more than likely going by what is on a census record...for example, in Adam's case, US Census records show that he was born in France, nothing else.
I just did a quick glance at Bayern, Germany on Google search...I think it would be helpful to you to try to learn the history, and in doing so you might be able to figure out how to find records that may be there. More than likely, the only records you might find are church records (i.e. Baptismal)