Yes, I agree about the difference between coaching and facilitating, and I briefly mentioned that the two approaches I highlighted ("Option 1" and "Option 2") are almost like the distinction between "Facilitating Mechanics" and "Coaching," so I consider the videos to as much (if not more) about coaching as facilitation.
The challenge is that contexts are different and "coaching," if I can say anything categorical about it, is always about context. So, some specific examples can help, like yours about stopping after an objection is invalid, although there are also situations with new groups in which I might not do that.
Instead, I wanted to convey the general "coaching" energy or stance through some more generic principles like "grease the wheels" in addition to some concrete examples, so that people could then generate coaching interventions in their own unique way.
As I'm writing this, it occurs to me that one helpful coaching distinction I failed to share would be, "Beware of learning for learning sake," meaning don't explain more than necessary (i.e. "throwing answers like stones at heads who have not yet asked the question"), don't ask objection test questions you don't need to (because "I want to help them learn the questions"), and don't keep explaining something (or other options) if the person got what they needed to move on ("once you've sold, stop selling").
That seems to be a big part of effective coaching in my opinion.