This is what took me twenty seconds to figure out the 100% probability answer.
Yes, it took some extra seconds, but
I have a bag of tricks as I mentioned, and they work soundly within the spirit of the puzzle.
If you read my posts, I mention the worst of the scenarios re unlucky situations. Recall sitting to the left of a completely crazy all-in player much of the time, thus crippling your chances to do ANYTHING; and having an opponent heads up at the end getting AA twenty or 20,000 times in a row, while you have crap. Indeed, it took me 20 minutes to figure out how to get 100%. I realize you are skeptical, but think it through, get a bigger box, don't need to be high-falootin, be mid-falootin, then go low-falootin, if you need to, try to go falootin-free... you'll get there.
Your idea of tight play at the beginning of the tournament is correct. However, you don't have to be quite as conservative when you've built up a stack. Remember what Ivey says when he plays "without a plan." E.g., limping in when at least you know that an ace is out thus eliminating the ace high flush, and yes, that only helps a wee bit and maniacs can force you not to bother... etc.
What's the worst advantage you could have upon arriving at the heads up scenario given that you've had about 1800 hands to acquire an advantage?
Oversimplifying the problem, how many doubleups do you need to beat 5000 players?
(These two hints don't address your objection, obviously--they are for those who are still further from the solution.) Hope this helps. Your answer is one of the better ones.
I can't blame you for not seeing the tricks, so think again how to pound it from 99.9% to 100%, yes, it's a big leap and it's all the difference in the world. (I haven't forgotten my comments re 100 minus 10^-23 or 10^-80 or whatever it was... bag of tricks, real world, etc.)
P.S. your claim is not a proof.
In the words of the famous Canadian Prime Minister Jean Chretien,
"a proof is a proof, you have to have a proof."