I had it fixed by a local dent repair guy, who pulled it out from the outside. Apparently there are perpendicular brackets inside the C pillar, so it can't be popped out from the inside. He had all sorts of special tools to pop the piece out, and it took him 45 minutes. He said that it was especially difficult because of the size and location of the hit.
After pics:
Miami people: PM me for his phone number; the guy does excellent work.
Miro: Thanks for the offer.
Lester: I didn't witness the actual hit. But yes, the softball came from an organized league at a public park (Brian Piccolo in Broward), and the park manager said that he'd file a claim and the county would pay the repair. But when I called the county's risk management department, the guy there said that the county isn't responsible. Lots of runaround from local bureaucracy.