So, my opinion is that to make a tournament out of this, some of the randomness needs to be taken out, or a "free" solo (or an easy draw, etc) needs to be worth less in the tournament score system. A couple of quick thoughts:
1) Increase number of games played:
Playing more games lessens the effects of the random starts, so having a high number of games in each stage helps balance. That said, I'm thinking in the realm of 10-15 games per stage, which is quite a lot. And like I said, since solos are high value, even two great starts out of ten games would almost guarantee a player a spot to advance.
2) Randomize, then standardize, the maps for each pool:
This might be my favorite approach. The first game for each pool of four is entirely random. After that, each of the next three games include the same four countries, but with different players in each. Then, at the end of four games, each player has been each country once, and how they did relative to the other players becomes more of the focus. This could use the same scoring system, which I would rather not change.
3) Tone down the score system/points spread:
If the finished game were a hypothetical group, mapu would be at 3, while the rest of us were at -1. I like the focus on solos, but that may be too big a mountain to climb. The only real way out of that pit is by soloing. In a round of four games, you'd need maybe ALL draws, none of which could include mapu. Meaning all a player has to do is solo once and then get one draw in the next three games to advance. In a normal tournament, that's perfectly fine. But when that solo or draw can be "helped" by getting a lucky starting position, it really doesn't prove that any skill is involved. Now in our case it was a skilled player who soloed, but I'm saying that the solo didn't definitively prove the skill level. The toned down system could be something like:
Solo-2
2/3 way Draw-1 point
4 way draw/defeat/survive-0
We could also do a system that includes half points, say 2(for a solo)/ 1.5(2 way)/ 1(3 way)/ 0.5(four way)/ 0(defeat & survive). These both reward solos, but to a lesser degree. That said, I'm not a huge fan of this idea.
All in all, I think Idea #2 could definitely solve all the problems. And would still be sufficiently random and fun. Let me know what you think!