So, first of all, this was a very well written post and a unique topic to touch upon. I think it's clever that you transferred the energy from our conversation into this forum.
Notwithstanding my previously discussed objections to the initial quote (lol), I think your tips seem pretty useful. Smiling and gauging body language before the initial approach gives you a sense of whether she is receptive to conversation at the moment. Introducing yourself to the entire group portrays you as sane and friendly. The quick pitch and exit shows that you respect the fact that she's out with her girls and you're respecting their space. This all reflects effective communication. Whether you get a cal or not all depends on the woman at that point, but it's still a good approach.
With that being said, the pointer in your post that stands out the most to me is your "quick pitch" suggestion. As a man, it usually doesn't cross my mind that approaching a woman and handing her my number is even an option lol. I think it's a product of the "men are the hunters/pursuers" mindset. With that in mind, I think that when myself and the guys were discussing this scenario in our initial conversation, we all were envisioning the "getting her number" scenario instead of the "giving her my number" scenario. The "getting her number" scenario requires us to be in the physical presence of her and her friends for long enough to build rapport and then make the ask; which typically requires a bit of time, and is why I think so many of us view it as an unpredictable situation subject to "group dynamics" lol.
Your advice definitely stems from an understanding of the viewpoint of a woman and one of the things I like most about CRF is that it's a space where we can communicate across the gender lines. Great post!