If Teddy Roosevelt's spelling reforms stick, Queen's English and American English would look very different in writing, perhaps enough to create a sense that they were really different, though closely related, languages.
Have Americans standardize English spelling based on phonology.
The short essay "Meihem in Ce Klasrum" (Mayhem in the Classroom) is an example of how standardizing English spelling could change the English language. As the essay progress, it slowly changes out the letters used for their "new" spellings. At the end of the essay, what would originally be:
"Even, Mr. Shaw, we believe, would be happy in the knowledge that his dreams finally came true" becomes:
"Even Mr. Yaw, wi beliv, wud be hapi in ce noleg cat his drims fainali keim tru."
In this language, Y = SH, C = TH, and other changes in the language in order to simplify spelling. It's easily readable, once you learn the spelling conventions. I think if this type of reform was carried out, American English would be thought as a different language from British English.