Hey Kevin - I've been swamped and so haven't had much time to contribute to this thread, but you've seduced me into sharing a thought with that awesome question... :-)
Sounds like the organization would benefit from both of those worlds, and I don't think they're incompatible. Holacracy's focus on each individual having clarity and ownership of what outcomes (projects) they're trying to achieve is just to encode a basic GTD practice. It doesn't preclude multiple people owning and driving toward that same outcome in the same (or different) roles, or that outcome being a small step towards a larger outcome that many roles are all collectively owning and driving towards as well. You can simply use project requests to capture all that, or in many cases a Strategy might really help get the result you're looking for too. You can also have a project held by the overall Circle (since it's just a role in the larger circle), and just make that transparent as a circle-level initiative that all roles are requested to support as makes sense to them. And finally, to get people helping each other even beyond their roles, you could consider how you can encourage more Individual Action in the culture - i.e. people acting outside of their own roles to help with those circle-level projects and Strategies. At H1, we have a badge people can earn for taking Individual Action outside of their normal roles to help with a significant larger initiative.
Hope that helps!
Oh, and one broader thought on Medium in response to some of the other questions here: I think they're a good example of the "Stopping Short Syndrome" I wrote about in my book, as one common pattern seen when implementations don't stick (and maybe at least something of an example of both of the other patterns as well). As one data point there, when I visited them last year, they were looking at Lead Link as a full-time job, and it was a high-status one in their culture, which they celebrated when people earned - both of those are big red flags. I think they were running parallel power structures - management hierarchy and Holacracy - and I don't think that's a stable or sustainable state. I'm surprised they lasted as long as they did like that...