I have the OFHS BAN03 cd of transcripts which includes Claydon and apart from the marriage entry (which I believe you know but have shown below) there is no other mention of Elizabeth there or in any other parishes on that cd.
1813 Aug 27 Anderton William bach to Elizabeth Hardyman, spin botp by license.
Witnesses Wm Miller Astell Beere
Interesting it states both of this parish although neither has baptism is in the regs. The info for the parish states that this is the most northernmost parish in the county and the last before you cross the borders to Warwickshire and Northamptonshire. It might be worth a post on rootschat for these two counties.
Sorry couldn't help any more. (Sadly I don't have BAN01 or BAN02)
Regards
Steph