Let me update you on what I have, nearly a year later...
Henry was born about 1830 in Massachusetts. He did, in fact, mary Cecelia Ann Mills on 24 Mar 1853. I verified the LDS information two ways. Henry and "Celia" had two children that I know of--David, born 1857, and Ida May, born 1859 (died 1909). She appears on the 1860 census with the two kids, but it doesn't list her marital status and he is not listed, either.
Somewhere I found that his father's name was George W. Bucklin (1801-1880), but not the son of Theodore mentioned in Stormont's book on p.649. That George W. was a physician who lived in New Harmony and Muncie and was born around 1840. However, I am trying to make a connection between Henry P. and this Bucklin family, since David (grandfather of Theodore) was an early pioneer of Gibson Co. from the east coast.