Ok, you made me break out my Beckett research book because I've looked into every Beckett that was in Kentucky around the time of Thomas' birth. The marriage between John Beckett and Nancy Frye was Oct. 1798 and I have this John in Bourbon Co. in the 1790, 1800 and 1810 census. They are very possible parents, but no proof yet.
The John in Harrison Co. married Jenny Fleming in Sept. of 1798 and I have a note that Harrison county was too far west to make them possible parents plus they were in Harrison Co. in the 1800, 1810 and 1820 census.
There was a Benjamin in Clark Co (1800) and Estill Co. (1810) which again is too far west to be possible.
The second Humphrey that stayed in KY was born 1761 and died in 1839. He married Mary Shreeves in Feb 1786 in MD. He appears in the 1800, 1810 and 1820 census for Fleming Co. KY and the 1830 Census for Lewis Co. KY. Possible but probable given ages of parents??
There was a Samuel in the 1810 census of Mason Co. with two sons under the age of 10, so he's a definite possibility.