julie,
This sure is a tough one!
I know it's a long shot but have you sent away for the birth record for the Catherine Gibbens whose birth was registered in Isle of Thanet between April - June 1838, just in case Catherine was mistaken about her birthplace?
In the census after her marriage, was there ever a Gibbons living with her? Or a niece or nephew that didn't belong to her husband's side of the family?
I tried looking under Fitzgibbons, too, just in case, but no luck.
There are several deaths for William Gibbens in Thanet between 1837-1852.
There are also deaths for William Gibbons (various soundex spellings) in Greenwich in the same time frame.
I was wondering if perhaps Catherine's father had died and it wasn't noted on her marriage record. What if the mother remarried and Catherine was enumerated under a different surname?
Or what if Gibbons was Catherine's stepfather's name and not the surname she was registered under? Still, we should be able to find them in 1841 & 1851.
I'm sure you've thought of all of this.
I hope someone can look up the parish records for you. They don't seem to be on the LDS website and it looks like they don't have microfilm of Anglican baptisms for the time frame you want. (Someone please correct me if I'm wrong.)
Regards,
Josephine