Here is a good explanation of how the yeast work and why you shouldn't bottle or keg too soon.
http://www.brewgeeks.com/the-life-cycle-of-yeast.html
---Thank you for the article! I am definitely in no rush to keg. The article reinforces my plan to kick back and let the yeast do their thing.---
In your second video it appears that the sensor for your temperature contoller is just loose in the freezer. While this works pretty well it would be even better if you control the temperature of the fermenting beer instead of the air around it. Put the sensor against the carboy, a little insulation on top of it, and tape it to the carboy so the sensor is below the top of the beer.
---I plan on doing that for my next brew, as stated in my first post. It seems to be a solid concept, for sure.---
I can't tell what beer you are brewing but here's some generalities about making better beer. Very light colored and low alcohol beers mature quickly but they still need a little time to mature after the fermentation is complete. As you go up in alcohol or toward darker beers, the time to mature goes up. Make a dark beer with high alcohol and the time really goes up.