In other words, the extrapolation of the experiment to the general case ([from your post] "that is true of anything one can ever think or feel") is, in my opinion, not inevitable.
It is also probably necessary to distinguish between choosing what to think about, and choosing/deciding what the contents of a thought will be. The latter seems to create a problem of infinite regression to me. If we define free will to be the ability to consciously decide not just what to think about, but also what precisely to think about it, then we cause it to be impossible by definition. Why do I say this? Because decision making requires criteria, and criteria, in this context, are thoughts and ideas themselves. In other words, you require a different conscious entity, with pre-existing thoughts and ideas, to decide upon the specific thoughts and ideas of the conscious entity in question.
I think a lot of the nature/nurture talk is people trying to reconcile the impression that they're a free mind shackled by some sort of natural predisposition. From your point of view (correct me if I'm wrong) a human being IS a natural process, and so the distinction between so-called freedom of thought and genetic predisposition is irrelevant - whatever our beliefs about the way our minds work, thinking/acting is simply a natural process within a natural world, and it has a natural explanation and origin.
I'd be really interested to hear your views on fate, actually. Do you believe in it? If so, what form of it do you believe in? And in what way does it not necessarily lead to fatalism? Belief is perhaps an inadequate word here; it implies choice. I suspect you view belief in similar terms to myself - it's a compulsion born of current understanding rather than a decision.
I'm not sure how coherent any of this post is - I'm writing this in between bits of work (and eating lunch!) so I probably don't have time to do it justice. Additionally, this is not really my area of expertise, so much of this is simply "as it occurs" to me.