I have had a theory (maybe it's just a hypothesis [an hypothesis???] at this point) that any song can be sung either to I am the Very Model of a Modern Major General or to When I was a Lad (and Now I am the Leader of the Queen's Navy) - sometimes to both. Amazing Grace seems to fit nicely with Major General. Not so well with When I was a Lad, though it can work with some shoehorning.

Don