How did we (USA) so it with copyright law?

Because there were large corporations using their political clout to make it a number one issue for your administration.

Your administration then made copyright law changes a central goal of many agreements - essentially a non-negotiable requirement for say a trade agreement to proceed.

We didn't. The WTO copyright framework is a joke that only goes after sports rebroadcasting and people who watch Disney movies for free. Meanwhile every valuable piece of US science and industry has been replicated on the other side of the planet and used for great success.