The actuator rod was bent and wasn't sliding the ignition switch out far enough. Straightened it out, replaced the switch, and had to tighten the switch down with only one screw because the back screw would cause the switch to pull away just enough to keep it from starting with the key fully turned. I could have lengthened the hole for the ignition switch a little more, but I got lazy. Hopefully that helps someone in the future. Despite the typical shifter wiggle start being caused by a faulty neutral safety switch, it can also be caused by actuator rod and ignition switch interactions.