I honestly don't think the C's with Irving and Hayward ends up much different as neither of those guys is a carry the franchise type player and they both probably still aren't on the team.
Bias is always #1 and I think not getting Duncan with the best odds will always be #2.
There are a couple around the summer of 2007 and the 07/08 season, that I think could have altered Boston's history a lot. First, what if the ping pong balls don't land on 5 and instead land on 1 or 2? Do they still acquire Allen or Garnett, or just build around Durant or Oden (with Pierce, Rondo, etc.)? Second, let's say the ping pong balls still land on 5 and the Allen trade is still made, but what if they don't acquire Garnett and instead go into the season with Big Al, Allen, and Pierce and instead use some of those assets to acquire Pau during the season, likely keeping Al in the process. How many titles do the C's win with Allen, Pierce, Jefferson, and Gasol (obviously the Lakers don't land Pau in that scenario)?