I appreciate people giving their thoughts to solving this problem, as it's something that I have discovered greatly affects the outcome of games. Me and two of my friends played a series of games, none of which we were in at the same time. We recorded wins, and whether we went in the first or last half of turns. The games were a mix of most gametypes (Full varients besides Full Attrition Pick and Full Attrition Borders were not represented. 1v1 and 1v1q were not represented, and neither was Conquest Hardcore Random or Borders. All games were upgrades disabled. All games contained six or more players). Out of 27 games played, we won 8, drew 4 and lost 15. 6 of those 8 wins were instances in which we went in the first half of the turn order, as well as three of the draws (though that seems less significant).
While I understand that this isn't a statistically significant number of trials, it does suggest a trend. I would encourage a few other people to experiment with their win ratios and the turn order, and possibly post results. Again, I reiterate I don't really care how this issue is solved, but would like to see it solved somehow.