There is a difference between SAT and SAT Subjects. SAT’s can be and are gamed. SAT Subjects test knowledge and analytical skills. If you take Subject tests, they’re all multiple choice, but there’s no “gaming the test” (perhaps in Math?). And there are Ap’s if you don’t like multiple choice tests (I don’t like them either, I find essays more reflective of real mental work, but I also see them as a necessity, ie., you know exactly what you want to know, even if you won’t know what the student wants you to know… Those are two different types of tests.)
You can also try AICE and Cambridge PreU tests which are even more essay based than AP tests. Exams are in November, you’re expected to take 3 “principal” subjects or 2 AS + 2 ALevels.
http://www.cie.org.uk/programmes-and-qualifications/cambridge-advanced/cambridge-pre-u/qualification/
http://www.cie.org.uk/images/347131-june-2015-question-paper-2.pdf
http://www.cie.org.uk/images/149235-specimen-question-paper-2-for-2014-onwards.pdf
http://www.cie.org.uk/images/149237-specimen-question-paper-3-for-2014-onwards.pdf
http://www.cie.org.uk/images/339440-2019-specimen-paper-3.pdf
http://www.cie.org.uk/images/348246-june-2015-question-paper-41.pdf
http://www.cie.org.uk/images/151482-specimen-question-paper-1.pdf
http://www.cie.org.uk/images/348460-june-2015-question-paper-11.pdf + http://www.cie.org.uk/images/356411-june-2015-resource-booklet-paper-11.pdf
No idea if you can self study the complements you need in a couple months, nor how you can register for them.