I'm not sure this will help or not. Sometimes knowing what's not there does!
1. In Muhlenberg County KY Marriages I found
25 Aug 1814 - George Godwin to Nancy Hunsaker by Asher Shelton
2. In the three Deed Abstract Books on Muhlenberg County (by Brenda C. Doss) 1798-1850, there were NO Godwins mentioned.
3. The same is true of the early Will extracts for the county.
4. I have extracts of the 1799, 1800 and 1810 Muhlenberg County KY tax lists taken from the Muhlenberg County genealogical quarterlies and I found no Godwins mentioned for those three years. In 1810 there was a John Gladwin 02001 20010.
The following might be helpful: https://familysearch.org/learn/wiki/en/Kentucky_Taxation
You possibly might find something you could get through your LDS library.
Dorann O'Neal Lam