Fixed it! After five hours.
Here is a tip for all future sway bar installers without the necessary hardware and a mild mental retardation: The nuts go INSIDE the LCAs. The bolts go all the way through, but the nut threads on in the middle. I figured that out like 3 hours ago.. But I had to go back and uninstall and reinstall it again.
And after extensive road-testing, I can say that: sway bars kick ***!