Agree with RScottie, you can always go down the lawsuit lane.
Wait, is Geico your insurance or his? Go after his insurance first.
Or have the teenager pay. If he wants to avoid big lawsuits and a big insurance premium hike, have your lawyer ask for cash and a release of all liability to keep it quiet "for his sake". They often jump on that, for obvious reasons.
I understand the insurance company's view, though. Your vehicle made contact with terrain. No collision involved. They won't admit that dumping the mike might have actually saved you from injury (and 5-digit medical bills) but then again, they're in the business of COLLECTING money, not handing it out. So you gotta find an angle that will make them pay out.
This thread should help (I am sure you're not the first one to go through such hassles) and again, a good lawyer should be able to claim some damages.
Keep us appraised of the progress, please.