How to approach American English vs. British English spelling in a paper? I am currently writing a paper, for which my title and core problem is spelled differently in American and British English. 

I don't worry about my professor preferring one way of writing over the other, as I'm not residing in an English-speaking country, but:

After all, my paper is being written in English, even it won't be published. Thus I wonder:

Is there a "standard procedure" for such cases, at least in US Ivy League universities or in certain citation styles? (I am currently using APA, 6th (our prof. didn't prescribe any specific citation style) as it suits my personal preference of how a reference should be cited and displayed.)

I will definitely mention both words in the "keywords" area, but other than that I will go with one spelling, namely the American English one. The word is "harmonization", if that should be important.

Sorry for my lack of initial research, I found this SE question though.
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...