If scheduling a true 16 car race for this tournament becomes too much of an issue, I came up with an idea that might possibly work.(While on man's thinking throne

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We would break the race into your standard tournament ladder.
Each race will be a broken into a 1vs1 race. The two people in the race will be responsible for setting up the perfect time for them to race. They'll have from Friday to 10PM Sunday EST to conduct the race, and determine a winner. This will make 8 1vs1 races in the first tier. Winners move onto Tier 2 section A, Losers Move onto tier 2 Section B.
Tier 2 will consist of 4 1vs1 races in both A and B. If you lose in Tier 2, you'll be eliminated. Winners in Tier2A go onto Tier3A, and the same goes for the B side.
Tier 3 will be 2 1vs1 races, and Tier 4 will be 1vs1 race. The winners from Tier4A and Tier4B will move onto the final race, with whoever wins, winning the tournament.
Here's an example Assuming that the player on the left in every race wins. It was made with construction paper, a marker, a red pen, and a whole lotta love.
But yeah, this is just an idea if it proves impossible to get 16 person races due to time constraints.