I think a lot of that is also 'court vision' and looking at where your other players are as well as their defenders, rather than just the guy guarding you and the one or two who will step in on you if you're able to beat your guy. And that also has to do with just practicing several basic moves (dribbling skills, pivoting skills, moving the ball around) so that you don't even thing about any of it - it's all natural movement, so that you can completely focus on the other stuff happening on the court.
If you have to 'think' about the move you're going to make, you're not able to do much else with the ball but focus on that specific movement. This always seemed like what happened with Woodbury in the paint, too - he started overthinking what he was doing with the ball instead of reacting and having the muscle memory to play more naturally. He'd focus too much on 'making the move right' than just trusting his training and being able to find an open guy. Woodbury was a pretty good passer, but not a big post scoring threat. Both Pemsl and Cook seem very natural and relaxed with post moves in the paint - that's something that lots of big men can take a year or more of college ball to develop, particularly against comparable talent.
I always liked Woody, and felt like he wasn't ever reaching his full potential, for whatever reasons.