I'd like to have the Curl records you referenced as well. My Charles Botkin 1738-1820 married Jemima Curl who we believe is sister to this William.
As for Wm. being the son of Jeremiah and Mary (McCreary) Curl I can offer land records that show Jeremiah and Mary Curl sold land in Job Weltons tax district in 1777 after purchasing that land in 1772. This was in Hampshire then Hardy now Grant Co. (W)VA. There is a Jeremiah Curl mentioned at West's Fort in 1778, which was in Harrison Co. WV about 20 miles S of Clarksburg on Hwy 79.
My Charles Botkin, his brother Richard Jr. and William and Jeremiah Curl (believe this is Wm.'s brother) where living in Job Weltons Tax District in 1782-1785. My Charles Botkin and William Curl then move to Lost Creek WV 1791, which is just a few miles away from West's Fort. They stay here until the 1803-1805 time frame and then move to OH.
I have a picture of William Curls Tombstone in Logan Co.
I can't prove Jeremiah's wife's name is McCreary but the land record does state Mary.
As you can see both Wm. Curl and Charles Botkin stayed close to each other starting in 1782 and eventually moved to OH together. You wouldn't have any information on siblings of Wm. would you?