3 minute protest is used very often in college sailing and team races. It works fine unless you have someone in the room like Sam Seriously though, we used to do it right on the finish boat, works great.
I've umpired high school and college team racing, so no, you probably don't want to be in the room with me
The big difference between that and this is you have pro or semi-pro judges on the finish or umpire boat making a decision, and another big difference is these rules experts see the incident in real time. At the high school level, the boat has coaches from opposing teams and a third unbiased judge. At the college level, it's professional umpires in the boats making the calls and hearing the on-the water protests.
A 3 minute shootout on the beach isn't going to work. I agree with Jake that we would be better served by conference calling/Skyping judges into a hotel room.