i work as an SAT tutor part time for kaplan.
i took the SAT three times. first two times i didnt prepare at all and still managed to do ok. but my mom signed me up for some private tutoring sessions and i improved my score by 400 points overall.
the SAT only really tests how good you are at taking the SAT and there are definitely tricks and strategies that can really help.
id recommend tutoring rather than taking a class. i dont know what company youre taking classes with and if you would even be able to switch from a class to one on one tutoring but if you can i would suggest you do. its much more personalized and you can really focus on the specific areas where you can get the most points