The problem with any project like this is that English simply has way too many variants, dialects, accents, or whatever you want to call them and categorize as. It's the language with the highest number of speakers in the world, by a long shot, when you include people who've learned English as a second language, of course depending on at what level of proficiency you're willing to call them "speakers of English". Everyone seems to want to learn it, and there's hardly anyone in the world who has no knowledge of English. It's used as a lingua franca whenever there are people who can't speak one another's languages. Some countries whose population speaks various languages, like Uganda, use English as their common language.
In today's era of globalization and with the ease of communication with anyone around the world provided by the internet, these "variants" have mixed, merged, and interchanged making it nearly impossible to talk about "American English" or "British English" as somehow homogenous variates, separate from each other. Even people from the same area can speak English differently, especially when you factor in their age, level of education, or even just personal preferences. I've met Americans who use "typical British expressions", as well as Brits who use "typical American expressions". There's lots of gray area.
I guess what I'm trying to say is that I don't think one person can do this all by themselves. It would require an extensive survey and lots upon lots of grunt work that would have to be done over many years of meticulous study. Otherwise, you'll end up with a list of differences that will be very arguable because there will always be at least one native speaker of one of the varieties you've described who will simply say "I'm a speaker of this variety and I don't speak like that".
