I took the redesigned SAT without much preparation. I got an okay score- slightly above average. I have four months until my next SAT test date. I am now using Khan Academy as my sole SAT prep. I took a practice test from Khan Academy and I improved by 70 points within the first few days using Khan Academy. I am still using Khan Academy for my SAT prep; is it possible I could improve by 300 points for my target SAT score?
It's definitely possible to improve by 300 points on the SAT with the proper prep methods. You have an especially good chance of reaching your goal because your first score was the result of taking the test without any prep. Students who aren't as familiar with the SAT tend to improve rapidly without any changes in content knowledge as they get more accustomed to the structure, content, and timing. Since you have four months before your next test date, I'd recommend scheduling out five hours of studying a week until you find yourself consistently scoring in your goal range on practice tests.
You should also try to use other resources besides Khan Academy to hone your skills. While Khan Academy is a solid resource in certain respects, it also has numerous shortcomings that limit its effectiveness. It doesn't provide actual testing strategies, its lessons aren't complete enough to clarify difficult content, its divisions of Reading and Writing skills are flawed, and the question explanations are often weak. Read more details about these issues here.
To supplement your work with Khan Academy, consider getting one or two good prep books and reading our tips on how to get a perfect score (even if you're not aiming quite that high, they're still helpful!). Keep in mind that the most important thing you can do when studying for the SAT is carefully analyze and correct your mistakes on each practice test.