How, exactly? I've done everything I can think of to boost my team up in the rankings, but I haven't budged much from middle of the pack (5th place-ish). I'm starting to think the beginning of the season determines all, and there's not much movement after that.
You're sort of right.

Whoever gets Lebron is going to get a bucketload of guaranteed stats all across the board. Anyone who has Dwight Howard will get rebounds, and suffer in FT%. If your drafted players are busts, or if players stop being "profitable", then dump them.
I
plan on catching up by constantly adding players who are playing above average, and dropping players who aren't. I have 1 elite player, 3 very good players, 2-3 guys I want to keep because they have their ups and downs, and the rest of the guys are good at 2-3 key stats --- 3-pointers, blocks, rebounds, or assists, while ALSO not hurting you in FG% or FT%. If those guys stop being productive, I drop them. That's why I have 30 transactions.
Basically:
1. Get players who can help you 3 key stats, while also getting somewhere at least 13-16 PPG, because that's what the average player on each team in our MacRumours league scores. They also MUST have a decent FG% and FT%. If they're VERY good at 1 or 2 categories, I don't mind if he only scores 10 PPG, or even less.
2. Blocks are the hardest numbers to get, then 3-pointers, then steals, then offensive rebounds. If you're going to pick up guys who specialize in a stat, he may as well do 1 or 2 of these things well.
3. EVERY player I pick up needs to be good at FG% and FT%, since you can't "catch up" in those stats. I make an exception for players who don't shoot FG or FT often (e.g. Marcus Camby), since they won't ultimately hurt you. Guys who shoot often AND have a low FG% or FT% are bad (e.g. Kemba Walker, Dwight Howard) because you can't make up for their inefficiency by getting another player who shoots 180%.
I'm not saying that I will be successful, but this is what
I am doing.