If this works for you, I think that's great. But I'm not sure this is the right approach for everyone. I know it's not something I could adopt.
(Quoting with Re: because quoting normally on this device is causing trouble.)
I prefer just one or two actions per project, so I organize my projects accordingly. I'm not saying you should organize yours that way, just describing ways that one-action can work with complex projects.
Addressing your example with this in mind:
Re: "Every year we'd host a chili cook-off fundraiser...
...calls to make, emails to send, creating spreadsheets, errands to run, things like that."
I would treat the fundraiser as multiple projects, possibly a dozen or more. Each of those projects would have just one or two actions.
Re: "I don't think it would have been efficient to make a call, for example, and then have to fish through project support to find the next call to make"
Instead of fishing, I would create a calls list as part of the project support material, and each time I realized I needed a call, I would add it to the list. That would allow me to have Next Actions that look like, "Make some calls," instead of "Call Fred" and "Call Joe."
Similarly, I might have a computer actions list.
I realize that this suggests, "Um...in that case, why not just have those as actions, set their contexts, and be done?"
Because I like to keep my actions lists short. Whenever something can be grouped as a list and gotten out of my everyday what-to-do-now lists, I'll do that.
Re: "I'm also not sure how I could limit the project to a "predetermined number of potential next actions.""
I don't think the idea is that you limit the project or predetermine the actions--in fact, Kanban is closely tied to Agile, which very specifically does NOT predetermine the actions.
I think the idea is instead that you limit the number of active actions in the lists that you look at several times a day. Kanban has the concept of a backlog, which I see as moderately analogous to GTD's Someday/Maybe, though I think of it as "Later/Not Today" rather than "Someday/Maybe."
Re: "but if they're not reflected in my system somehow, my mind would take back the job of managing my stuff."
In my view, if they're in project support material, they are reflected in the system, you just don't have to scan through them every day. I realize that your mind may demand that it see all those actions frequently. My mind freaks out and runs away if it sees all those actions frequently.