be.

$150 seems low. That would not even cover a flight (presuming you'll need to fly), much less accommodations while you're there. I think it would be reasonable to ask (nicely) for more.

To echo what Ibycus said above, judging from what you say here, it's unlikely that your stated research interests were vague enough as to hurt your chances of admission. In fact, I think (and I've heard this from several professors) that being too specific with respect to one's interests actually hurts one's chances of admission. This is so for two reasons. First, programs are looking to produce philosophers––they're looking to shape their students' interests and ways of doing philosophy. If you indicate that your interests are more or less fixed, this may suggest to an admissions committee that you may be less receptive to their molding/guidance/indoctrination. You're applying to be a student, not just a researcher. Second, I think indicating that your interests are more or less fixed on a specific area reflects a certain lack of humility, as least with respect to applicants who are applying straight from undergrad. After all, if you only have your undergraduate degree, then you have in all likelihood only scratched the surface of the discipline. If so, then how could you know that you're only interested in area x when you've never come in to contact with areas y and z? This second point presumably doesn't apply as much to applicants who possess an MA. My point, then, is that you probably did nothing wrong with respect to your personal statement. I hope you get an acceptance from that last school! If not, keep plugging away at that writing sample, if you're inclined to try again next year.

I can't imagine AW matters much. They'll have your writing sample, so they'll presumably judge your writing ability based on that.

I think your AOI might make a difference. If you want to do, say, Ancient, then your quantitive score may not matter much. By contrast, if you want become a logician, then your quantitive score would plausibly have more of an impact.

Option 1 is probably best. That said, don't force it: if the argument doesn't require, say, another six pages or so, then you shouldn't expand it just for the sake of making it longer. Doing so would likely result in an unfocused, tedious paper.

A heads up: Bill Lycan is pretty close to retirement, if not already retired.

I agree that it doesn't need to be double-spaced. I suppose your formatting choice, to some extent, will depend on how long your paper is. If it's on the long side, perhaps single-spacing is okay.

Double-spacing is, I think, standard for the writing sample. For example, NYU asks for 20-25 pages double-spaced. With respect to margins and font, it's probably best to keep it simple: Times New Roman with 1-inch margins.

I may be misunderstanding your post, but the implication seems to be this: most––if not all––of the programs ranked in the PGR are "top" programs. This is not so. Many of the programs ranked by the PGR could be classified as "mid-low tier." For example, the University of Cincinnati is plausibly a mid-tier program, but it is nevertheless ranked in the PGR. (I don't mean to disparage Cincinnati; it seems like a great program for someone with the right interests, including mind.) My point, then, is this. If you were to apply only to PGR ranked programs, you would not thereby apply only to top programs. As maxhgns points out, group 5 of the mind specialty rankings contains many solid mid-tier programs. Take a look at the faculty of those programs, and see if any have faculty whose work aligns with your interests. This is especially important for mind, because it's a fairly heterogenous sub-field. Good luck!

The New School should be off the table. Unless you are independently wealthy, do not pay for graduate school in philosophy. With respect to Texas Tech, $2,400 isn't terrible, but it is still a lot of money.

A Master's degree (especially one from a distance-learning program) is not sufficient for securing a professorship at a US university or college, including community colleges. You'll need a PhD for that. I would strongly advise against distance-learning programs in philosophy. The job market is bad, and having received your doctorate from such a program will hurt you. Online programs are not well-respected, and philosophy is (unfortunately) a prestige-sensitive discipline. Moreover, students from programs in the UK, I have heard, have a harder time on the market than do students coming from US programs. However, you needn't worry about UK programs not being "nationally" accredited; people from, say, Oxford often get hired in the US. Since you didn't major in philosophy, you will have a very hard time getting into PhD programs. So you should take a look at some funded M.A. programs in the US, many of which are tailored towards students who lack significant training in philosophy. Georgia State, University of Wisconsin-Milwaukee, and Northern Illinois are a few excellent places to start. Programs such as these will help you get into a good doctorate program. They will also give you some time to make sure that you want to spend 5+ years of your life studying philosophy.