When reading the U.S. Constitution, you must apply the language consistently THROUGHOUT the document. Thus, when the people are referred to in one clause, you must apply the same definition to each and every instance in the document.
For that reason, the Court's majority opinion in Heller nor MacDonald rejected your reasoning and their ruling is based firmly on how the word is used throughout the document such as the Tenth Amendment and "People" has always been interpreted as a synonym for individual rights. Collective rights are referred to via the states (the guarantee of the republican form of government for example). For example, your definition of people would make the right of assembly fit only for groups in the First Amendment and the 4th Amendment search and seizure provisions not applicable to individuals. Thus, the whole warrant provision would not literally make sense using your reading. It would also make void the right to vote for the House of Representative and the U.S. Senate along with killing any meaning of the 9th Amendment.
Scalia wrote the majority opinion and he is most careful with his historical and textual analysis. He has even written several books about the practice of deciphering what texts mean in a legal sense that are informative. For additional reference might also want to check out the English Bill of Rights from which our Bill of Rights is derived as well and Blackstone's Commentaries on the matter. In addition, the state constitutional protections that existed before the Convention also were interpreted as individual rights. None of them support the idea that it is a collective right.
BTW, that is why the high flown language of the former Soviet Union's constitution which appeared to grant freedom of speech, religion, etc. was routinely ignored is because these were collective rights of the people but belonged to no individual. Since punishment is individual, that meant that society possesses to right to terminate an individual's right on a whim. The better language for such things is a privilege rather than a right.
There is better historical support for the idea that states possess a collective right to form militia. However, as the Court's opinion in Heller notes, that consistently any such states' rights or limitations noted in the Constitution specifically refer to states and NOT people. Thus, the militia clause merely informs one of the reasons why the 2A is a necessary limit on the federal government (and applied later to the states via the 14th Amendment's fundamental freedoms due process jurisprudence.) Should be via privileges and immunities clause but that is an argument for another day and a change in Supreme Court's Slaughterhouse interpretation.
This is from the Court's syllabus of Heller,
" 1. The
Second Amendment protects an
individual right to possess a firearm unconnected with service in a militia, and to use that arm for traditionally lawful purposes, such as self-defense within the home. Pp. 2–53.
(a) The Amendment’s prefatory clause announces a purpose, but does not limit or expand the scope of the second part, the operative clause.
The operative clause’s text and history demonstrate that it connotes an individual right to keep and bear arms. Pp. 2–22.
(b) The prefatory clause comports with the Court’s interpretation of the operative clause. The “militia” comprised all males physically capable of acting in concert for the common defense. The Antifederalists feared that the Federal Government would disarm the people in order to disable this citizens’ militia, enabling a politicized standing army or a select militia to rule. The response was to deny Congress power to abridge the ancient right of individuals to keep and bear arms, so that the ideal of a citizens’ militia would be preserved. Pp. 22–28.
(c) The Court’s interpretation is confirmed by analogous arms-bearing rights in state constitutions that preceded and immediately followed the
Second Amendment . Pp. 28–30.
(d) The
Second Amendment ’s drafting history, while of dubious interpretive worth, reveals three state
Second Amendment proposals that unequivocally referred to an individual right to bear arms. Pp. 30–32.
(e) Interpretation of the
Second Amendment by scholars, courts and legislators, from immediately after its ratification through the late 19th century also supports the Court’s conclusion. Pp. 32–47.
(f) None of the Court’s precedents forecloses the Court’s interpretation. Neither
United States v.
Cruikshank,
92 U. S. 542 , nor
Presser v.
Illinois,
116 U. S. 252 , refutes the individual-rights interpretation.
United States v.
Miller,
307 U. S. 174 , does not limit the right to keep and bear arms to militia purposes, but rather limits the type of weapon to which the right applies to those used by the militia,
i.e., those in common use for lawful purposes. Pp. 47–54."
Thus, whatever the states may do, the Supreme Court has declared the right of the people to bear arms as an INDIVIDUAL right.
