No problem. I followed my own family roots to the 1600th too and the Beulich Hammes' are not my direct line but ancestors of two women roots. You were very lucky with your research, congratulation. Hammes is a surname that appears all along the river Mosel and the regions of Eifel and Hunsrueck near to that river. I think it developped in more than one village. It may be a patronym of the male first name "Haman" or "Hermann". I don't know by sure, but because of lots of scannings by myself I suspect it may be connected with the confessions there. The name appaers in catholic regions/villages as Hammes with "s" an in protestant regions/villages as Hammen with "n".
By the way I don't think you will be able to find document being older than the 1600th. The parish registers in the villages started about 1630 to 1670 or even later and the surnames of the ordinary families (not the nobel) developped not earlier than the 1500th.