I think more than anything, I think the only thing you are missing is the equivalent of “skating” in Jasmine’s paper. Here’s what I mean:
When she was talking about the different uses of the space and how skaters would “edit” it to suit their needs, that was always in reference to the fact that they were there to learn how to skate. You had relationships of experts teaching novices, etc., but all in the context of learning to skate.
If we go to the example of the cafeteria, here’s the one question I’d ask you right away: What is being learned? I think we could even take your own example. You sat there and slowly realized just how unwelcome you were in that space. Now, I think you could take this one step further: What are the kids learning in the cafeteria? Yes, it’s there for eating, but that’s probably not what is being learned there.
To me, I think the most interesting question you could be asking is how does the cafeteria serve as a space where children learn the “social” aspects of school: what groups hang out with what groups, who the cool kids are, whether or not they fit in to a group, etc.
Armed with a question like that, then I think you could apply a lot of what Jasmine talked about into your analysis. For instance, the very fact that the chairs aren’t fixed is an interesting thing, right? It allows students to reshuffle the space, making bigger or smaller groups at will. How does that change how one can “learn” about the school’s social pecking order?
I also think a lot of the L&W LPP framework could apply as well, depending on what you observe. There certainly might be students who are “experts” at the lunch social scene, and some which are not. Is there a gradation? Does the lunch room or other school spaces help you see how that transition would take place?