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This seems to be a legitimate project.
My biggest concern is will this have a negative impact on my site (the original) in the long term. In other words, is there a chance that Google might see the content on the LOC archive and think that my site is the duplicate?
You should ask them more about their intentions and whether they have thought about how to handle the duplicate content penalty.
Remote chance they would be aware of "Duplicate content penalty" :)
Though your page should be protected again dupe content since it was indexed first, if their PR is too high (naturally acquired PR I mean), then they might rank ahead of you, for the article page.
Better you ask them to disallow spiders to the page they intend to add. Just a small line of code will do it.