All of the above is the secret to being a fast programmer when you are sitting and writing code. If you are caught up all day in reading email and going to meetings, then no programming happens whatsoever – that's a different problem.
Still, there are some analogous solutions you could try. Perhaps the organization does not fully understand you or your role, which is why they're sending you so much email and putting you in so many meetings. Perhaps there's something about the organization that you don't fully understand, such as how to go to fewer meetings and get less email. Maybe even some organizational difficulties can be resolved by adapting the solutions in this post to groups of people instead of individuals.
-Max