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I should have known better. You were absolutely right, after Adaware finishes it's scan, it allows you to view what it is about to quarantine. I opened up the "Negligible Items" and scrolled down until I found the "Internet Explorer Addresses". I selected that one entry, and told Adaware to ignore it from now own.
I then selected everything else, and deleted it all, and when I opened up IE again, my history was still there.