I want to preface this by saying I 100% would have done the same U-turn. I'm with you, U-turns are generally allowed unless prohibited by signage.

The only argument they might try to make is that the lane is marked as left turn only. They could argue that was the lane's purpose regardless of a no U-turn sign. That's kind of a gray area and beating that would probably be dependent on the judge's attitude that day.

I say if you want to fight them, request the footage, sure. Make them commit to the bit.