I've not been looking at this thread and I'm not sure why I have come on to it now but a couple of comments on the etymology of "haul away".
I am not an expert on this subject but my guess is that the phrase comes from an old sea shanty (work songs sung on old sailing boats), such as "Haul Away, Joe". Commonly, the word "haul" means to pull something with great effort. On the old sailing ships, the raising of the sails was done by hand, as was the rasing of the anchor. These tasks were team efforts. The singing of sea shanties was done to help co-ordinate the efforts of the sailors involved, as they pulled together, and also to make the task seem a touch less arduous. The singing was led by the shantyman, not an official position but a much respected role, nevertheless.
Somewhere in my boxes, I have some old 1960s' folk music magazines from Liverpool called SPIN and they have a series of articles by Stan Hugill, a real expert on the subject of sea shanties and sailors' songs. I must dig those old magazines out some time. Stan Hugill wrote one of the standard books on the subject.
There were different types of shanties for different tasks and even different types of shanty for hauling tasks. A long haul shanty was used where a succession of "pulls" was needed, for example to haul on the ropes in order to raise the sails. Short haul shanties were used when there was a longer period of rest between each tremendous pull. Shanties were very rhythmic, rather like field hollers and chain-gang work songs, or even the chants used by the military when performing drills. Some of these hauling tasks on old sailing ships were undertaken in order to alter the direction of the sails to catch a change in the wind.
The word "haul" does also refer to changing a ship's course at sea but, at the same time, "overhaul" is a nautical term meaning to overtake or catch up with another vessel. Also, I believe old sailors would refer to the wind hauling southward, for example, meaning that the wind was changing to a southerly direction. Despite the slightly different usages in different contexts, I'm sure they're all linked.
None of this says anything about MK's new song, of course but here's "Haul Away, Joe":
http://www.acousticmusicarchive.com/haul_away_joe.html"Haul away" can also, I believe, refer to the ship itself moving speedily through the water.