Yes, Sid Calderbank is definitely your man for Jone o' Grinfilt. His 2006 CD Includes the following:

1. c1805 The original Jone O' Grinfilt or Jone's ramble or Jone's ramble from Grenfelt to Owdham or Jone O' Grinfield or Jone O' Grinfilt
...
5. c1819 Joan O' Grinfilt junior or The handloom weaver's lament or The poor cotton weaver or Joan O' Greenfield & bailiffs or Joan O' Grinfield
...

So he dates the original Poor cotton weaver to c.1819.