Harry Levi Parsons Clark Born 1857. This is posted in the family-line of a Ms. D Bell. I've looked at her list before, but the name Kernes is recently new to me so it didn't register. I attempted to contact her a couple times, but no luck.
You may be right about him being a son of LP Clark- so far his records show 3 wives and about 10 kids, but no Jr. I pulled up all the Clarks in Pope County 1880-1885, and didn't see any possibilities. I'll keep looking and check for any time gaps.
Ordering a copy of his 1882 marriage record with Mary Alice might solve this puzzle.