What's the timeline look like at these parts?
My guess is that the video file isn't as healthy as you may think. Playback and breaking a file down to editable frames are two very different beasts. Playback is very simple and even a very badly damaged file will playback thanks to redundancies. However, these don't add anything to the ability to edit the file, which will break down a file to it's constituent part and reveal hidden flaws.
I Think the problem is the you dropped too many frame out and the frame you kept are being played to quickly. Animated GIF file sizes are huge compared to video file formats and the color is much poorer then video. However Browsers animate them automatically and the can be used in links href.
I downloaded your gif and it looked like you started with a 1080p video. You re-size it from 1920 wide to 400 pixels wide and to make a small animated gif file size you dropped out too many frames. You file is still 2.3MB. I wanted to get some idea of what could be done. How much 1080p mp4 re-sized to 400px wide would fit into a 2.3MB mp4 file and if saved as an animated gif how big would it be and what would the quality be. Seems like only 5 seconds fits . Here is what I saw.
Sean 1080p mp4 14.6MB around 5 sec http://www.mouseprints.net/old/dpr/Sean1080p.mp4
Sean 400 w mp4 2.3MB size of your gif http://www.mouseprints.net/old/dpr/Sean400.mp4
Sean 400 Ani gif 10,7MB 5x your gif http://www.mouseprints.net/old/dpr/Sean400.gif
SeanDropFrames 2.3mb like your gif http://www.mouseprints.net/old/dpr/SeanDropFrames.gif User every forth frame.
The mp4 also includes the audio...... even the scaled 400 px wide mp4....