The biggest problem I see is that team 16385 would be at a massive cash advantage to team 16384 if that is indeed how many get into each tournament.
First, a key to what I am saying is that the 1st step is to get 16384 teams involved. As I said, I think all teams (or almost all) should be involved. How do you do this? Well, suggest some ideas.
But if you want one example, I played another online game where there was a top tournament (for the top 16384 teams) and then feeder tournaments for the remaining teams. You make less or no money in the feeder tournaments but you improve your world ranking so you can qualify for the top tournament the next season. The top teams in each tournament get seeded so they have no chance of playing each other until later rounds. But other than that, the draw is random.
You mentioned the disadvantage of the 16385th team, but that is offset by getting a very high seed in the feeder tournament, you can almost certainly go far and probably get seeded the next season in the top tournament.
Anyhow, just one approach. I am sure there are others.
Run of the Mill Canadian Manager