I regret I cannot remove any bricks from your wall. I know of one John Frith bpt in 1827 in Tuxford, Notts. An unlikely candidate for deportation in penal servitude, he was a schoolmaster and died, unmarried, in Doncaster district Yorkshire West Riding.
The only other person of that name known to me was John William Bancroft Frith, a joiner from Worsop, Notts. But he was born in 1860 which was already late for such deportations; moreover he was still living as a married man in 1901 in York with his wife and daughter.
I appreciate your problems and I wish I could have helped.