How do I improve my SAT from a 1470-1490 to a consistent +1500 in a month?

Find out what kinds of test questions you get wrong consistently. Work on those kinds of test questions. It’s really hard to get into the 1500s, since getting a very small number (maybe two to four questions) wrong can knock you out of the 1500s into the 1400s. Make sure you know the tricky grammar rules (“who” vs. “whom,” etc.), how to figure out reading passage questions, and how to handle the “tricks” in math problems. Those are all in any good SAT prep book.
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Try the “advanced” versions of common SAT guides (e.g., Barron’s SAT 1600) that are designed to help good students get as close to perfect scores as possible. Take the official College Board practice tests under timed conditions, if you haven’t already. If you have, use practice tests from books, etc. I can’t guarantee you a score over 1500, but this is the only way you’re likely to get it.