Wow, that seems like a huge PITA. We just do the same thing, but let the league do all the logistical stuff you have to manually do. That is pretty much exactly how our coach does league play so that's pretty cool. Lil SF bats toward the bottom and has gotten really unlucky with at bats so far this year. He has been on deck like 4 times when something has happened and he didn't get to hit. Tuesday night the storms in KC were coming in and i'll be honest, the 3 and 2 folks were pretty much waiting for a kid to get zapped before they cancelled the game. He was up and his DA friend got picked off ending the inning. He then got up and after the first pitch, they finally called the game. Coach had him bat at the top for the next game to get him and others more at bats. Even when coach does stuff like that we still kick the crap out of most teams in league play so I'm guessing if we are still on this team next year, we won't do league, but who knows. Tourneys can be brutal. I love it mostly, but its giving up a whole weekend so adding more will be tough.
It's not that big of a PITA and it's a very small tradeoff to being able to have complete control over our schedule. Date, Time, Location, Opponent, etc. I don't think a league would even be feasible for us. Also I don't know of any competitive spring/summer leagues in Omaha. All the leagues are just rec (which it sounds like maybe what your team is in since they're beating the doors off teams?). I know some of our peers will put together teams to play fall competitive leagues but we have too many kids playing football to make it work.