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Blackstone said that natural law wasn't written anywhere, and it was up to men to "discover" it.

The Founders did. That's probably why they used Blackstone as a starting point, not a blueprint.

But some late incidents having given rise to an opinion, that the common law of England, is not only the law of the American States, respectively, according to the mode in which they may, severally have adopted it, but that it is likewise the law of the federal government, a much wider field for investigation is thereby opened; of the importance of which, the general assembly of Virginia, at their session in the winter of 1799, have thus expressed their sentiments, in behalf of themselves, and their constituents.

"It is distressing to reflect, that it ever should have been made a question, whether the constitution of the United States on the whole face, of which, is seen so much labour to enumerate and define the several objects of federal power, could intend to introduce in the lump, in an indirect manner, and by a forced construction of a few phrases, the vast and multifarious jurisdiction involved in the common law; a law filling so many ample volumes; a law overspreading the entire field of legislation; a law that would sap the foundation of the constitution, as a system of limited, and specified powers."
St. George Tucker Blackstone's Commentaries

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They even thought enough of Vattel to use public monies -

Journal of the Senate of the United States of America / Monday / March 10, 1794 / Volume 2 / page 44
Ordered, That the Secretary purchase Blackstone's Commentaries, and Vattel's Law of Nature and Nations, for the use of the Senate.
http://memory.loc.gov/cgi-bin/ampage?collId=llsj&fileName=002/llsj002.db&recNum=42&itemLink=D?hlaw:13:./temp/~ammem_LF5V::%230020043&linkText=1

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Just as the Founders sometimes used Blackstone, they based the Declaration of Independence on Biblical concepts - because that's what the people were most familiar with.

But when it came the the Constitution, they used Vattel's Law of Nations, Or, Principles of the Law of Nature, Applied to the Conduct and Affairs of Nations and Sovereigns.