Crop a video with a moving crop area of fixed size
I recommend AVISynth (a script based video editor for VirtualDub) and the DeShaker plugin.

You can learn a minimum amount about AVISynth and simply load DeShaker, have it stabilize on the person's body and it will follow them smoothly as they move.

You will have a finished product that is stabilized as a bonus. 

You can also learn more about AVISynth, establish precise crops that are animated to follow the person, and get a perfect result (based on the quality of the input). You can set your moves with frame and pixel accuracy by typing numbers into the script and reloading the frame in VirtualDub.

It might be worth 5 mins. exploring those links to see if you want to try another video editor. 

If one of the current video editors you've installed has image stabilization you can try it, but DeShaker is one of the better free ones (as of a year ago) that I've used.