How did the Founders strike a balance between reserving individual rights and forming a strong and long-lasting government using the Declaration of...

The Declaration of Independence made the striking claim that governments were essentially established for the purpose of protecting the "unalienable rights" of "all men." Because Parliament and the British king had failed to carry out this duty, the Declaration claimed, the American colonies were justified in parting ways. The Declaration established the protection of individual rights as a founding principle for the new government. These principles were enshrined in most of the state governments, many...

The Declaration of Independence made the striking claim that governments were essentially established for the purpose of protecting the "unalienable rights" of "all men." Because Parliament and the British king had failed to carry out this duty, the Declaration claimed, the American colonies were justified in parting ways. The Declaration established the protection of individual rights as a founding principle for the new government. These principles were enshrined in most of the state governments, many of which included bills of rights and specific protections of principles such as habeas corpus. 

When the Constitution was ratified and went into effect in 1789, it did not include many specific protections for individual liberties. There were prohibitions against Congressional suspension of habeas corpus, punishment for ex post facto laws, and a few others, but the purpose of the Constitution was to establish a powerful central government. Protests by Anti-Federalists in the various state ratification conventions led to the addition of the Bill of Rights within two years. The rights protected by the first ten amendments to the Constitution do not need to be repeated here, but the Bill of Rights represented a compromise to satisfy those who were troubled by the powers given to the the federal government at the expense of the states, which were held to be more conducive to individual rights. 

As for the Freneau poem referenced in the question, it does not directly represent an attempt to strike a balance between government power and individual liberties. It does, however, celebrate these liberties, which Freneau says were established upon leaving Europe: "What wonders there will shall freedom show/What mighty states successive grow!"