The way I heard it, the progression is well preserved.

In Amsterdam there lived a maid, etc.
In Amsterdam there lived a maid and she was mistress of her trade.

I"ll go no more a-rovin with you, fair maid.

I took this fair maid for a walk, etc.
And we had such a loving talk.

I put my hand upon her knee, etc.
She said young man you're very free

I put my hand around her waist, etc.
She said young man you're in great haste.

I put my hand upon her patch, etc.
She said young man that's my main hatch.

In six weeks' time I was badly bent, etc.
And off to see I sadly went.