Sorry about the typos (spelling is not my best attribute).
Dunga -
I used the random list sort on that website you listed. I did not save the results, but I had to move a Poland team and Brazil team to the other side to avoid matchups. Otherwise it was random. Though if you want, you could just do it live like you said. Doesn't matter to me.
The only reason I used 'two' brackets is because the matchups are already that way for NCAA Basketball. made it easier to get the seed matchups correct. It also makes it easier to shift a team to the same seed based on same country matchups. You could just as easily have 32 seeds though, it would not effect where the teams are placed now though.
Here is one with 1-32 teams:
http://www.printyourbrackets.com/pdfbrackets/32singleseeded.pdf
The method I used was #1 team (Brazil) in top #1 spot, #2 (Italy) in bottom #1 slot, #3 (Israel) in bottom #2, #4 (GB/Ireland) in #2 top slot, etc. So I just snaked between the slots like that based on the vote results.