Apologies if I have missed something, but have you looked at Non-Conformist, specifically Baptist, records for the Hannants?
William Ward Hannant retrospectively registered his 8 children, with their birth dates (between 1794-1817), on the Buxton Baptist Chapel register, on 22 July 1833.
You wondered if William Clark Hannant, b. 21 Aug 1808, at Buxton, may be Hephzibah's parent.
When was his wife Mary born? When did they marry?
Given that William Clark Hannant would have been 29 when Hephzibah was born c 1837, may she have been either his, or their, illegitimate child, later "adopted" for propriety's sake?
This would explain why she has the Hannant surname.
Note (Although my Nor & Suff-folk, previously always presumed to be Anglican, appear on Established Church records, I subsequently found, to my surprise, quite a few of them had very detailed Quaker register entries, so I now routinely check Non Con records as well!)
Cheers,