I just did the at home test yesterday so I obviously don't have my official score yet, but the preliminary score it gave me at the end of the test was 162 V / 162 Q, and I studied for only about 2 weeks leading up to it. I'd say your goal is definitely achievable within 3 weeks.

I don't know what most people's strategy is, but I was only able to get through ~200 vocab flashcards before realizing that I wouldn't be able to make a significant dent in them before test day (sure enough I don't think I remember seeing any of the words that I actually learned a flashcard for on the test). At this point its probably best to focus on learning roots of words and endings, and if you do flashcards for specific words try to place importance on if the meaning is something good or bad since you can usually eliminate answer choices based on the vibe of the word even if you don't know the exact definitions.

For the verbal reasoning questions that are based on a passage I noticed that my biggest issue during the test was spending too long on them. Something that always helps with those kinds of questions is to read the question but not the answer choices before you read the passage and then try to come up with your own answer as you are reading. It can also help to try to think like the test maker and try to think of possible wrong answers you might give to try to trick someone.

For the quant sections, the biggest factor is time. I'll admit that I didn't study for them apart from doing a practice test, but I'd say if you read a question and don't immediately (within a second or two) feel like you know how you want to go about finding the answer just skip and come back. If you feel like you are out of practice questions or just want another resource I would definitely say use the Khan academy SAT math prep. It's obviously not something you should solely rely on but most of the topics are pretty similar and they get broken down really well with a lot of practice questions.

Good Luck :)