Henry's death record states father Henry Allen & mother Ruby Blake. As for his marriage records, he may have mixed up his father & grandfather's names. Or as you say his father could be a Henry Allen who moved away. A copy of the original death record may give some other clues. Have you looked for descendants of Henry B. Allen's children ?
I looked at 1850 census again and found William Taggert listed with, looks like Rebecca Black age 45 and Mary age 4 and think the census taker wrote Rebecca instead of Ruby & Black instead of Blake or as you say she could have had a middle name. I went through all of the pages for Ferrisburg, but she could have lived in a different town.
I lean more to your Henry Allen being from Obadiah Allen & Hannah Gage family mainly because of Henry living bu Pwrwe P. Gaige/Gage. Have you ever checked land records for Henry. When I looked at them I only photocopied Quit Claim's for Obadiah Allen & his son Joseph Allen as they did not have wills & died about the same time. On the rest of them I only copied from Index. I will keep looking. I plan on sending a copy of my Allen information to a libray in Ferrisburg area. A few years ago a Allen cousin[who lives in Danby area] from Obadiah & Robert Allen sister Abigail Allen who married Nicholas Curtis found will of Nicholas Curtis at court house that was not allowed becaus it was not signed. Eva