If you decide to take it again:
My brother (older than me by three years), has always picked-up (and remembered) math concepts better/faster than me. He can also do math problems faster. This difference is only noticeable because we were both involved in an annual math contest since we were about 9.
I placed higher (in my grade level) in some years than he did (when he was my age), though he usually did beat me, because I was better at not making stupid errors, he usually (always?) knew more material than me.
(We both took Calc BC as juniors, which is unusual in our district where the normal kids never can take it and the advanced kids take it as seniors)
My brother took the SAT four times before he could get his 800 in math (I think by the fourth time it was too late for some of his colleges). I got it on my first try as a junior in January.
End of "story"
I'm sure (if you're that far advanced in math) you know EVERYTHING on the math section (my brother did). The trick is to have confidence. I'm sure you finish going through the problems with lots of time left. You don't get any points for finishing quickly so just remind yourself the entire test that you have plenty of time and GO SLOW. Circle every important value as you read and re-check that you used those values in your calculations, before you circle your answer re-read the question (you may be solving for y when they asked for x), and just do general idiot checks.
Take a few math sections of SAT practice tests, get a sense of how much time you really have so you don't get nervous and go faster than necessary on test day.
(imoh) If you go back at the end and check problems you will rarely catch errors. The only time I notice is when I check immediately after finishing a problem.
Taking practice tests is also a great way to learn how you are making your mistakes. Is it reading the problem too quickly, entering wrong values, misusing calculator, thinking too quickly and making incorrect assumptions ect. ?
Make a list and tally-mark the number of errors and from what, then you can be more aware of yourself when you take it for real.
Of course a 700 is great, but I can see where you're coming from if you want a highly competitive STEM school.