We aren't exactly sure how districts will be bracketed if the system is implemented.
As such, I constructed a simple matrix to attempt to bracket things for this exercise.
In each of the classifications, the draws are broken into two 16-team sides, with four quadrants in each group of 16 teams.
In each of those quadrants, there is a first, second, third and fourth place representative qualifier from each of the districts, with one team from each of the four districts represented.
It is balanced in a way that you can't meet a team from your district prior to the quarterfinals and the earliest point that a winner of a district will face another district winner is also the quarterfinals.
The teams are not seeded here, but the seeds do represent something.
16-team bracket
Seeds 1-4: Winners of a District
Seeds 5-8: 2nd place teams in a District
Seeds 9-12: 3rd place teams in a District
Seeds 13-16: 4th place teams in a District
32-team bracket
Seeds 1-8: Winners of a District
Seeds 9-16: 2nd place teams in a District
Seeds 17-24: 3rd place teams in a District
Seeds 25-32: 4th place teams in a District