4: The Milking Payle
for 6 or 8 [presumably longways]
mms pages 6 and 7
Playford version: none
Music: Any working version of "The Merry, Merry Milkmaids", the Playford dance
Part 1
Verse 1, Part A
1: Lead up [a double]
2: [Fall back a double]
3-4: Set [and turn single, left]
Verse 1, Part B
1: Lead up [a double]
2: [Fall back a double]
3-4: Set [and turn single, right]
Chorus 1, Part A
1-2: The men set [and turn: step left, step right, turn over your left shoulder] to their partner (the women stand still)
3-6: The women do a hey ("till the end of the tune")
Chorus 1, Part B
1-2: The women set [ and turn: step left, step right, turn over your left shoulder] to their partner (the men stand still)
3-6: The men do a hey
Part 2
Verse 2, Part A
1-2: Side [left to line up right shoulders]
3-4: Set [and turn single, left]
Verse 2, Part B
1-2: Side [right to line up left shoulders]
3-4: Set [and turn single, right]
Chorus 2, Part A
1-2: The women set [and turn - step left, step right, turn over your left shoulder] to their partner
3-6: The men do a hey
Chorus 2, Part B
1-2: The men set [and turn - step left, step right, turn over your left shoulder] to their partner
3-6: The women do a hey
Part 3
Verse 3, Part A
1-2: "Halfe turne", *instead* of arming.
3-4: Set [and turn single, left]
Verse 3, Part B
1-2: Half turn again
3-4: Set [and turn single, right]
Chorus 3, Part A
1-6: "and then like as before", so as in Chorus 1 (men setting and turning, then women heying)
Chorus 3, Part B
1-6: As in Chorus 1 (women setting and turning, then men heying)
Conclusions:
We have a confirmation of the Moll Peatley instruction of "half turn" as an alternative to arming, though it still has to fill the same amount of time.  Considering that you do it twice, perhaps this is a "switch sides" maneuver? 
Or is it a "take arms, switch places, take other arm, switch back"?
Also of vast interest is the "for 6 or 8" instruction, marking a far more flexible framework for these dances than the ones in Playford in general.  The only real limitation to the number of people here is how fast they can do the hey, given the actual time allowed in the music.
Music: The structure of the music could either be an AABB verse-done-twice, chorus-done-twice format, in which case, there might well be 5 measures to the B part, giving the various heys a full 4 measure count (possibly vital when trying to complete a 4-person hey) if the setting is really supposed to be without the turning.
However, some investigation subsequent to my first reconstruction of this dance has revealed a more or less logical link between this dance and the Playford dance "The Merry, Merry Milkmaids" which provides music that works well, and irons out some of the questions about the chorus structure.
The two dances are not any more similar than any other ECD with a standard verse structure split by sets and turns, but there is a ballad link between the Milking Pail tune and the tune for The (Merry) Milkmaids which means we have a structure to fit the dance into, instead of a bucket full of questions.