You're going about this completely the wrong way. First of all, you're not getting into NYU for philosophy and NSSR offers horrible funding. Your best chance is an MA program.
Unfortunately, you're applying to the wrong ones.
For political, you're going to want to go to either GSU or UWM. UWM in particularly has an impressive placement record, and they're more likely to be sympathetic to your writing sample (though I would still advise against a writing sample on Confucius and Hegel, if you have something else available). You might also want to consider LSU, which fits your interests and background quite well, but their placement isn't very good.
Brandeis was initially designed for people who actually went to Brandeis, so while it's advertised as a 1 year program, you won't be getting out of there in one year if you're coming from a different university.
NIU is very analytic and with your sample, it is unlikely you'll get in. It doesn't matter though, because they're a horrible fit for you if you want to do political philosophy.
Despite (very) impressive placement, the funding package at Tufts is horrible. Unless you're independently wealthy, expect to go in debt. It is not worth going in debt for a PhD program, never mind an MA program. Also not a good fit for you anyway.
As for expecting a strong grasp of philosophy, just because they don't require you to have a BA in the topic doesn't mean they don't want you to understand the topic through, say, independent study. The point is to take students who would get in to PhD programs if they had the right background and give them that background.