Hmmm, interesting question: is the SPELLING (not the dialect, not the lexis, not the syntax, not the anything else) a fundamental part of an authentically-American narrative voice?
I think I'm going to say yes. Why? because if I'm reading the story, being asked by you the writer to believe I am reading the inner monologues of a 'real' American character who suddenly mentions the "colour of the sky" instead of the "color of the sky", I think I'm likely to register the British English spelling. And then I could be pulled out of the story momentarily, thinking ,"Why's this narrator spelling 'colour' with a 'u'? I though s/he was American."
True, many of your readers may not be as tragically pedantic as me, but then again some might. So, reckon you'll have to bite the bullet, start using far more 'z's than you're comfortable with, and sacrifice an entire syllable from the word 'aluminium'.
You got this, Jimmy. You got this.