Free software is a movement concerned with software that respects the user's freedom. A particular piece of software is either licensed in a way that respects the FSF's four freedoms, or it is not. Whether or not the author of that software makes a living doing what he pleases is a separate concern.
This question seems to ask, "How do I make a living writing software that complies with the four freedoms, but not by charging for support, selling warranties, finding a co-aligned charity/business to pay me for what I already do, or having software with some subset of non-free features?"
At the most basic level, people will pay you if you do something that supplies value to them. The catch, of course, is that what another person finds valuable may not align perfectly with exactly what you want to do.
I'll paraphrase a bit from an answer given by Richard Stallman which I heard in person and can't give a direct quote for:
Developer effort is an abundant resource, but the ability to direct developer effort is a limited resource. Developers are writing free software all the time, right now. But if you're a business, it might be that all of the software that exists in the world right now doesn't solve exactly the problem you need solved. You could, of course, wait (or ask nicely) for that tireless legion of free software developers to produce exactly the software you need, but odds are, they won't. They'll keep working on whatever they'd like to work on.
Now, if you offer money to those developers to redirect their energy into writing the software features that your business needs, then you might get somewhere.
(Apologies if I've misrepresented Mr. Stallman's viewpoint in any way above.)
Of course, if a company offered you a chance to redirect your efforts from working on your own your perfect dream of ideal programing projects to prioritizing the specific features that they need, maybe you'd consider this a failure to meet the requirement of doing exactly what you want. To such a response, I can only say: this is a fundamental economic difficulty that must occur anytime people with money have different goals from people who want money.
You might also say -- even if the tasks the business needs closely align with your own wishes -- that this is a violation of your prohibition against (analogously) "waiting for an NGO." But again, I submit that since economic transactions must involve two willing parties, you must necessarily wait until you can find a buyer for your services. This is no different from getting a job (you must wait until someone accepts your application) or selling a good (you must wait until a buyer will give you money).
