As promised above, I will update the status of this issue.
After a significant amount of work and also significant progress, I was able to connect to the live nest camera feed programatically but was never able to actually record the live stream into short videos, although this was easy for my MacBook webcam. My belief is that Nest has engineered this feed such that camera owners cannot directly access it, leaving no option but to use their "Nest Aware" monthly service. I do not want to do this as I do not want to pay for it and because I want to create options that Nest Aware does not offer.
Searching the web, it appears that this kind of thing might be done by using another software package, "blue iris". I did not want to get this either as I am sure that flexibility would be sacrificed and also the camera would need to be made publicly shared(!)
So I am giving up on Nest, although I like the hardware.
I did find an alternative. I also had an Arlo Q camera and I tried that, using an open source API on GitHub:
https://github.com/jeffreydwalter/arlo
I was able to access the camera and save motion detected videos to my disk within an hour of finding the above link. So, if you want to do this type of thing, I recommend Arlo over Nest.