Q is right; don't take McGrath's comments literally. "Last Goodnight" ballads were composed for sale at, or subsequent to, executions (often public executions, with therefore a good market available) and had nothing directly, as a rule, to do with the person condemned; just words put into their mouths by hack broadside merchants. One on Essex was available in print, it appears, within two days of the execution.

I don't have time to précis the details at present; maybe two ballads and two tunes, won't know till I can compare them. Won't be for a few weeks, so somebody else should do it.

See Simpson, The British Broadside Ballad and Its Music, 1966, pp 206-8 and 747-8. All the relevant information is there, I think.