I was happy to find this thread. I am less focused on publishing in journals (though of course that is an important way to contribute to the knowledge base) and more focused on applied research/field work. Basically, in my areas of interest, there is an enormous amount to explore and learn, and there are people and organizations eager to participate in the research, but not much funding to do so.
So far I am doing this through consulting. I have a notional budget and a reason to do the work, but I can spend way more time on it than someone who is chasing grants. But I'm not sure if this is a good idea in the long term. It's hard to partner with people who are working in the traditional model, and I feel limited to small-scale projects.
On the question on legitimacy, though people ask me what university I'm affiliated with, they seem to accept that I am working independently. I've also been lucky that my graduate school gives alumni decent access to journals for life. (By the way, I never got a PhD, for many reasons including the desire to work on more immediate/applied research, the need to make a living, and no interest in teaching or academic politics.)
I would love to hear from other people who are taking a similar approach.