This is a game of psychology as well as luck. If whales don't participate or if they give up because they are not the last entry, a small person can definitely win. Likewise, if bots participate, they will usually have a limit of how much they would enter before deciding it is not worth it anymore thus allowing a small person to win. The winner of this game could be anyone. It all depends on the risk thresholds for individual players regardless of whether they are whales or not.
And because each entry close to the deadline extends it, it would not be possible to just keep putting transactions into the game until the deadline. You are right though, the last successful transaction will be the winner.
It will maybe be based on luck at the beginning since the pot will be low and there would be less participants however as the pot grows then the whales and bots won't easily give up their positions, why would they.
Its similiar to what happened with Bitcoin when it was created. You could get BTC for free back then just by visiting some faucets. There was a 1 BTC per day faucet back when BTC had no open market. So small people did get lucky if they got the free BTC and kept it till today. However today since BTC value is so high there is no free 1 BTC faucet. H
So if the pot grows very very large it will get very competitive and eventually only the whales could profit off this. I wish you best of luck, but I don't see this idea really being successful.