Or was addressing the king a stylistic choice? That is, everyone knew policy was coming out of parliament but addressing a bunch of complaints to a nameless parliamentary mass isn't as compelling to the drafters' internal American audience as targeting the king?
No.
First of all, most of the signers of the Declaration of Independence had a great deal of legal experience, and a very sophisticated understanding of the British constitution, and they came up with extremely sharp legal arguments to advance their interests. It is also the case that the British constitution at the time had many aspects that were "undefined" so many of the constitutional arguments that the colonists made were concerning things that were contested. But everything they did had a legal and politics purpose to it.
And remember that they won in the end, and the American Revolution was as much a legal and political war as a military one.
The decision to address the Declaration of Independence to the King was consistent with the colonial understanding of the British Constitution. It was the position of the colonies that because their charters came from the British monarch and that because the colonies had no representation in the British Parliament, that Parliament had no authority to impose legislation on the colonies. Obviously Parliament disagreed and argued that it was sovereign and this led eventually to the British constitution giving all real power to Parliament in the 19th century, but in the 18th century the role of parliament in the British Empire was still open, and by ignoring Parliament in the Declaration of Independence, the colonies were holding on to the position that Parliament had no right to legislate for the colonies, and so whatever problems existed were the fault of the King.
The Declaration of Independence should also been seen in the context of the Olive Branch Petition. The Olive Branch Petition attempted to appeal to the King to take action on the theory that everything wrong was done by Parliament and the King's ministers. By the time of the DoI, the colonies had given up hope so that the Declaration of Independence was directed at the King.
Aside from constitutional theory, there were good political reasons for blaming George III rather than Parliament. The colonists had friends in parliament such as Rockingham Whigs and Charles James Fox and there were many in Britain that were sympathetic to the colonies, and who saw George III as an aspiring tyrant. Focusing the Declaration of Independence on royal tyranny rather than parliamentary tyranny gathered the colonists support in England which ultimately convinced the British to give in after Yorktown. So rather than being ignorant of British politics, the Declaration of Independence was designed to (successfully) gain the colonists maximum support in Britain.
This should all be seen in the context of the evolution of parliamentary power. Formally, the laws are adopted by the King-in-Parliament. Over the course of centuries, real power has moved to Parliament with the King as a formality, but much of this happened in the 19th century, and in the 18th century, the King was still somewhat of an important actor in British politics. The current situation in which the monarch was merely a figurehead without any real power was not the case either in theory or practice in the 18th century. In particular, George III could and did influence the composition and actions of Parliament through royal patronage. Ironically, it was the loss of the colonies and George III's ill-health that led to Parliament asserting more powers against the monarch.
It's very important to understand that the current situation in which the monarch is a powerless figurehead was not the situation in the late 18th-century. More subtly, a lot of British constitutional history is written with the idea that the loss of power of the monarch was "historical destiny". It's important to realize that this view of history only came into being in the 19th century, so in the late 18th century the idea that the king had no power, the king *should* have no power, and that the king *would be destined* to have no power would have been alien to them, and they had no idea that this is what would happen in the next century. It's very clear from current scholarship that George III was in fact heavily involved in colonial policy so I don't think that having him share some of the blame is unfair.
Having said that, *how much* real influence George III had and *how much* blame he should share is something that is surprisingly controversial to this day.
There are many ironies in this situation. Accusing George III of being a tyrant was effective because he was not an absolute monarch in the vein of Louis XIV, and therefore something like the Declaration of Independence could get real support in England. Although the Intolerable Acts were passed by Parliament, the colonies focused their ire at the monarch as to not alienate their sympathy in Parliament. Finally, the colonies in the Olive Branch Petition were asking George III to use his perogative powers to override parliamentary authority in the colonies, but George III refused to do so because he felt bound to enforce the will of parliament.
Anyhow.....
After the Declaration of Independence, Parliament attempted to concede some of these points to the colonies in the Taxation of the Colonies Act 1778. But by then it was much too late, but the concessions and constitutional arrangements Parliament made with the American colonies ended up influencing how the other parts of the British Empire.
So the eventual way this was resolved after the American Revolution, was to hold to the position that sovereign power in the colonies came from the King to be exercised by the King's ministers, but that Parliament has the authority to legislate for the colonies, but this power is to be used only under rare circumstances with respect to a colony. British colonial practice is has been that Parliament usually gets involved only to set up constitutional structures and to basically declare that a colony is no longer a colony. Also trying to tax a colony was such a disaster with respect to the American colonies that they never tried it again.
The notion that colonial sovereignty comes from the King, is exercised by the King's ministers, and that parliament is something of a bystander when it comes to colonies, turns out to have been legally significant in one court case involving Hong Kong. When Britain transferred the exercise of sovereignty from Hong Kong to China, the laws that went with sovereignty (i.e. were created under the authority of the King) were transferred over to China under Article 8 of the Basic Law. However, parliamentary legislation involving Hong Kong lapsed, and this turns out to be significant at least one landmark court case - Democratic Republic of the Congo & Others v FG Hemisphere Associates LLCFACV No 5 of 2010 (8 June 2011)1 & (8 September 2011) 2CFA.
see: The British Constitution and the American Revolution: A Failure of Precedent Precedent. William & Mary Law Review - March 1976
George III and Parliament, October 2011, Parliamentary History 30(3):395-413. Harry Dickinson
https://www.doj.gov.hk/eng/public/basiclaw/basic14_3.pdf - Democratic Republic of the Congo & Others v FG Hemisphere Associates LLCFACV No 5 of 2010 (8 June 2011)1 & (8 September 2011)2CFA
In a monarchy, the King is not only the head of State, but he is the embodiment of the State itself and of its principles, so it made sense to address His Majesty for what was seen as major wrongdoings by the government. This was not like going to higher authorities, as George III was unlikely to intervene in Parliament or against the government for such an issue, but it was a symbolic gesture signifying that the core principles of the British State were at stake. The same is still being done today when, for example, members of First Nations write to the Queen when they get into an unsolvable dispute with the Canadian government :