Prof. Smith gave a detailed and honest answer to which I don't really have anything to add. But two things about your question struck me. First, your GRE scores seem to combine two different scales: the current scale on which Analytical Writing is scored out of 6 and the old scale on which Verbal and Math (Quantitative) were scored out of 800. Nowadays, Verbal and Quantitative are scored out of 170. Did you take the GRE on different occasions separated by some years? In any case, an Analytical Writing score of 6 is 99th percentile, as is a Verbal score of 780. Those scores should impress anyone who sees them. Second, I'm struck by your having published a book on philosophy and skepticism before even entering a doctoral program. I'd be surprised if any of your competitors have done that. If the book is good and the publisher is reputable, you'll certainly stand out from the crowd. My only concern in that case would be whether you think you still have much to learn about (say) skepticism from a doctoral program after having already published a book on it. If you have time to email me the title and publisher of your book (my email address is on my homepage, linked to at right), I'd be interested in knowing more about it. In any case, best wishes.
Nearly all of the philosophy journals practice "blind review" of submitted articles. What this means is that those making the decision to publish or not to publish the contributed piece have no idea who the author is, or what his professional status (or lack of it) might be. So yes, it is certainly possible for someone who is not a professional academic to publish philosophical work where professionals will read it.
Even so, I think it will be difficult for someone without specialized training to get published in this way--the rejection rate at most philosophy journals is very high even for those with graduate training and years of experience, so getting one's work published can be quite challenging, and usually requires that the piece to be published demonstrates mastery of the field and the most recent work in thsi field.
As for how someone might keep up with what is going on now, many publishers (I would recommend Oxford University Press, Cambridge University Press, and Blackwells, who all publish such works) have excellent collections of work, selected by an editor who is presumably an expert in the field, who chooses articles to include on the basis of their special impact and current relevance to study in that field. Purchasing (or borrowing from a good library) books of this sort and reading the articles included in them is an excellent way to "catch up" with what is really important in the field right now. Obviously, reading what appears in the most competitive journals (such as The Philosophical Review or the Journal of Philosophy) would also be very valuable. One who has read and understood well the works in such recent collections, and has also read and understood well the recent work in several of the main journals in the field, who thinks that he or she has a contribution to make to the literature could then reasonably submit a paper to one of the journals in the field and know that the referee(s) will not be prejudiced by the author's lack of professional status, because of blind review.
I am not sure what an "illegitimate" form of philosophizing would be--though different forms can be of varying quality. I also see quite a bit of activity at this website that looks to me like philosophical counseling, and I do think that philosophers are better equipped than others to handle most (if not all) of the questions that get posted here. Plainly, there are issues that would be better suited for psychologists (or psychiatrists, or other physicians). But looking around this site should provide pretty good evidence that we are able to answer--or at least respond intelligently and with certain special skills--to some kinds of questions (namely, philosophical ones)!