I had this idea, which might be impossible in practice, but I like the idea so I'll share it.
What if, instead of having four players per team play six games each against each other, we had a team of four (or whichever number works best) players connected to each other through Skype (or another platform), making the decisions together, and playing a total of six games against another team? The captain of each team would be the one to actually do the clicking on Goko, so that he would have the final word on everything in case there was a disagreement, and he could do some trivial stuff such as playing Villages before Smithies on his own to make the game faster.
The problem here, of course, is that finding a time when all 8 players are available could prove to be difficult, especially if the tournament was played with national teams like the previous Team Dominion tournament was. You can reduce the difficulty by using three-player teams, especially since I think that four players might be a little overkill for this kind of tournament anyway. That would mean less people whose schedules have to align, and more people that can be used as replacements. If you mix up people from different countries in each team, it might get a little easier, too, since there won't be the inevitable match where two teams from totally different timezones have to play against each other, but that might make it more difficult to communicate, since then the teams wouldn't necessarily have a common native language.
Another problem is that someone would have to organize the tournament.
What do you think? Would it be possible to pull this off in reality, or just on paper? Is the idea even interesting enough to try out?