Since they can't get through the whole lineup twice a game, I guessed they are a poor hitting team in general (and perhaps struggle to get off the field on defense). In that case, I think it would be wise to try to manufacture runs at the the top of the order to build momentum, gain confidence and put pressure on the other team/pitcher.
Actually, DDs team is a pretty good hitting team...with a few exceptions. During a bracket game with a short lineup, it's not hard at all to get through twice. It's the shorter-timed pool games with a fat lineup that's the problem. Most of the tournaments we play have 3-5 pool games.
The number-cruncher in me says that if you get higher average / higher OBP people more at-bats than the poorer performers, your team performance in those areas will be better, and that usually correlates to more runs. The art is distributing the power to make the best use of those baserunners.
However, I also understand the "good batter at the bottom" lineup philosophy, and it can be productive when you have hitters in the 1-2 hole that can hit the ball hard. Although I might not do it that way, it's a viable strategy, and not really the problem. It's batting behind a handful of players in pool games who don't perform, and although we might win the game, we don't get to that #12 spot twice.