Instead of committing to getting the requested assignment done as soon as possible, factor in some buffer time and ask for a couple of days or a week. 

This will help you get the work done along with any 'reactive realities' that come up, and it's a win-win if you get it done before the deadline.

Rather than having habitual meetings, make them dynamic and result-oriented. 

Focus on the problem, and ensure there is a continuous follow-up, giving people space to brainstorm and come up with solutions.

You need to figure out when your brain works best and get heavy work done in those productive hours. 

These windows of 'brain time' cannot be wasted with meetings and chores that end up wasting your time.

We normally get frustrated and can have a frowning expression when we are interrupted while being busy. When saying a 'no' can be impolite, a better way is to say 'yes' and then asking respectfully to fix a time to discuss.
The best leaders know the value of time and are proactive and purposeful in handling their daily calendar.