The challenge is "get me to change my position on the second amendment and firearms." Sounds vague enough that the only way to win would be to convert him from a rabid pro to a rabid anti. This isn't meaningful, it's posturing.
It's no different than your straw argument, Tom, that gun control can work. You postulated a lowering of gun-related deaths in the context of banned firearms. If that theory holds any water, it could be a submission to the contest.
He's offering the money for a logical, irrefutable reason why gun control trumps the second amendment's purpose. If the anti's think they are right, now is the chance for one of them to prove WHY.
If he gets a response which proves empirically that gun control is better than a right to keep and bear arms which he can't logically counter with facts, I'm sure he'll concede.
The only reason this might be considered posturing is, we all know no such logical argument for, or example of, successful gun control exists. It's like offering a reward for a DoDo Bird.