You should realize that this is a tall order. Most people who apply successfully in English use a 20-pp. research paper that got an excellent grade in an upper-level or graduate-level seminar. I would strongly suggest that you think about funded master's programs (there are, in fact, funded master's degrees in English) or about taking another year, doing an upper-level course or two in English somewhere, and then applying next fall.
That said, if you do decide to apply this year, egilson is absolutely right about getting advice and expanding an old piece. Beyond that, your best bet is to find a published article of about 6000 words to use as a model. Study it very carefully; see how it's organized, how it incorporates secondary material, and how it makes use of close reading. Then try to imitate its structure and evidentiary practices as closely as you can. I'm way out of your field and have no idea what journals publish on science fiction, but a little light googling reveals that there's an organization called the Science Fiction Research Association. They have fora over there, too; you should try asking your question over there.
http://www.sfra.org/forumYou should be doing a bunch of secondary research to support your argument anyway; that's one thing that distinguishes a 20-pp. paper from a 5-pp. paper.