I stayed up last night and wrote a slightly technical walkthrough of the game theory for the smart contract solution.
For anyone taking the “outside view” and assuming that the argument must be wrong, I’m sympathetic! But so far I haven’t seen how. The crux is that Smart Contracts allow you to burn money in an ex post incentive compatible way. I actually wrote about this functionality here on this site a few months back.
If a smart contract can burn money, it can change the payoffs in a coordination game and commit to a certain strategy. This is a very old idea, and my claim is that smart contracts just enable this generally. I think I made a mistake in my earlier posts–given that this is a forum full of engineers 
--to be a little loose about what the smart contract needs to do. All it needs to do, in the game theory solution, is set your money on fire if you don’t win.
The only fundamental technical problem that I can see being relevant is the Oracle problem. But, the on-chain outcome of a certain identity/wallet/etc. winning the F3D jackpot seems like a very strong oracle. Of course, there are security issues, common knowledge issues, and “repeated game” issues as well so, while the solution is evidently there, it won’t necessarily be easy to implement.
One final note per @ablebakercharlie I really don’t think dividends matter. Existing dividends matter, but once the game is solved nobody should purchase a new dividend. Given that the equilibrium solution requires the purchase of only one key, it seems that any new dividend would be out of the money.