It was a bit of a winding process, but essentially early on in my career I learned that I fit this[1] description very well. And stumbled upon the same fact that patio11 did: it's incredibly hard for most companies to consistently fill that type of role. And now that I have a history of succeeding in those types of roles, it's a lot easier to talk my way into new ones.

That said, you're spot on that the core of what I do is data consulting, although most of it falls under a domain-specific name and has been W2, internal consulting roles. I'm actually in the process of switching my full time role to a less demanding one so I can focus on ramping up my actual consulting business.