The only info I could find on William Goodwin comes from a website by andreas osiander.
William Goodwin (1720?- 1784) was organist of St George-the-Martyr at Southwark before moving across the river to St Bartholomew-by-the-Exchange in the City of London in 1766.
In 1774 he "inherited" the posts of organist at St Saviour's Southwark (now Southwark Cathedral), St Mary Magdalen Bermondsey and St Mary's Newington Butts from his father.
This piece sounds fine on the Frechilla organ with its split keyboard, which offers the possibility of "simulating" 2 keyboards by using different registrations for the lower and upper half of the keyboard.
In my edition of this work by Les Editions Outremontaises the registration for the introduction states: Diapasons and for the fast second movement: Cornet or Flute.