As a non-native English speaker how can I improve my SAT score?

I took the June SAT and got a 1340 (RW 540, Math 800). My goal is to get my RW score to 700+ by the August SAT.

Right now I'm planning to finish all of Khan Academy's SAT RW content, go through all the questions in the College Board Question Bank, and review vocabulary.

What else would you recommend? Are there any books or study methods that helped you improve your SAT Reading & Writing score?

Also, is it worth using third-party materials, or should I mainly stick to official College Board questions? And would memorizing vocabulary from Word Smart be helpful, or would my time be better spent doing official practice questions and reviewing my mistakes?

I'd especially love to hear from other non-native speakers who managed to raise their RW scores a lot in a relatively short amount of time.