Since small file size is the goal, you may have better luck targeting it with average bitrate mode rather than guessing at quality parameters. You may also have to significantly downscale from 4K footage to something more portable like 960x540 or 1280x720. I’m quite certain the 3’57" video from the net was not 4K, which contributed greatly to its small size.
The math to find the average bitrate that fits your needs can be found in this thread: