Thanks for the steer on Jeremiah Grant. This changes things quite a bit. A quick search reveals a bar called "Jeremiah Grant" in Portlaoise in Ireland. Their website has the following story of the "legend" of Captain Grant: https://www.jeremiahgrant.ie/the-story

It seems that Edinburgh may be a miss translation of Maryborough (Grant being the last man to be hanged in Maryborough gaol in Portlaoise).

"Sheltering McKay or MacKay, or Mackie" seems a reasonable although I can't find any reference to a villain of that name in the Portlaoise area in the early 1800s.

Still no thoughts on Lord Natty Takeup but some progress at least.