Lina, I like your letter. I would not take out anything, except:
"Hey, you may not have even heard of the SAT before this"
Because, your letter is beatifully written and from the heart. I think it is very impactual because of this. But that last statement sounds antagonistic even if it isn't meant to. The placement at the end of the letter leaves the last impression to be a bit antagonistic, which deflates the impact of the whole letter.
I sincerely recommend leaving the rest as is. Also, I recommend showing it and discussing it with your parents beforehand. As a parent, I wouldn't want to be blindsighted by a call from school without prior knowlege.
Also, if the letter is effective in getting the administration to revisit the issue, your parents can be prepared to handle that phone call.
I hope your parents are supportive of your efforts. It seems clear that this is very important to you.
Good luck.
