That latest set of words doesn't fit Playford's "Stingo" tune. It's probably intended for "The Malt Man Comes on Monday", a 9/8 jig which i think was first published in Scottish sources of the mid-18th century. Here's a slightly later version, from the Gows' Second Repository. The first strain is the relevant one. (Staccato and slur marks omitted).
X:1
T:The Malt-man
S:Gow's Complete Repository book 2
M:9/8
L:1/8
K:G
D |E/F/GG G2g dBG| F2A AEA TF2D|E/F/GG G2g def|g2G G>AG G2:|
c |Bcd efg dBG|TF2A AEA TF2D|dBd ece def|g2G GAG G2:|
d//e//f/|g3 Tf2e dBG|TF2A AEA TF2D|gag Tf2e def|g2G GAG G2:|
If I remember right James Oswald really did a number on that, with lots of added sections.