Well, consider my problem solved. Took it to a wheel shop who has the Hunter GSP9700 (google it, you'll never go to a regular balance place again) and they showed me my tire as it spun and it was a tire problem. But it was drastically helped by being balanced by this machine. So, I'm very impressed.

The headache is gone, now the car deserves a wash, maybe a wax if I feel like it.