Point of information. Regarding entries for 'Fifeshire Fencibles' in Hythe birth records, this will be a reference to the Fifeshire Fencible Cavalry who moved to Kent from Essex in 1799, (having made their way gradually south from Carlisle in 1796 via Sheffield and the Fens). My g.g.g.g.grandfather commanded a troop 1794-1799.
There are detailed muster rolls and paylists for the F.F.C- biannual 1794-97 and monthly thereafter- at WO 13 in the National Archives, Kew. This may repay investigation if you haven't checked already.
It's dusty work, I warn you. I have just spent a couple of days in the company of my ancestor and his Laddies- "I venture to say there are not two finer troops in the regiment- I may say the ARMY". He didn't make it to Kent, though. Unfortunately he took sick the previous winter, went home and died.