Jeremiah Burris (with various spellings of Burris) shows up in the tax rolls transcribed on line in years subsequent to 1810 also.I don't have a Jeremiah Burris elsewhere in my research, so I am unsure what, if any, link there might be.
In more established links, I have seen Burris spelled several different ways.The fact that many people during this time could not read or write makes many of the records and research interesting, to say the least.
I agree that Claw is an unusual name that does not appear often in historical records. I am aware of the transcription at the LDS site but have not done anything towards looking at any original documentation.I note your comment about one other Claw marriage recorded.
I have been considering and looking at variations of Claw such as Clow, Clough, Clay, etc to see if any connections could be made, but nothing has even come close to establishing a link.
Thanks again for your followup to my query and the information you provided.