How to approach American English vs. British English spelling in a paper?
I typically don't worry about this question as a writer.  For what it's worth, I'm based in the United States, so I default to American English.  I always spell check my papers, but in the more than 25 papers that I've submitted, I've never gotten any feedback about using American spelling rather than British spelling; this question is very relevant for me since many of my papers are on graph colo(u)ring.  It may be useful to note that in the journals that I submit to and read, I've seen both American and British spelling.  (I think many editors typically let the authors choose which they prefer.)  

So my suggestion is this: choose either American or British spelling and stay consistent throughout your paper.  Don't lose any sleep over this.  It will not be the deciding factor in whether your paper is accepted.

However, for doing a literature review, I feel your pain...