Private School -> Public School lowering my GPA

I transferred from a private school with a unique way of calculating GPA to a public school after my sophomore year. The private school calculated GPA like this: A+ (97-100) was a 4.3, A (93-96) was a 4.0, A- (90-92) was a 3.7, B+ (87-89) was a 3.3, etc. if the class was an honors class, you would get 4 points added to your grade (89 would become a 93 and therefore a 4.0, 93 → 97 = 4.3, etc.) and 8 points for APs for a weighted GPA. With this scale, I had a 4.182 weighted and a 3.936 unweighted and was near the top of my class.

The public school that I am now attending gives 10 points for APs and none for honors, and uses an A (90-100) = 4.0, B = 3.0, etc. scale. My freshman year, at the private school, I got 3 89%s in honors classes because getting a 90% really didn’t matter much more, but because of that, my GPA plummetted to about a 3.7 with the new school’s transcripts. I have really high grades now, as a junior, at this new school, but since I went to a different school for 2 years, my GPA is far lower than many people who I have way higher grades than.

I have hopes of MIT, Stanford, CalTech, Princeton, etc., but I am really concerned this new scale is going to reduce my chances. My ECs, standardized tests and other factors are at those school’s level. I know they will be informed about my school change and everything, but I find it difficult to say that they would spend that much time analyzing my transcripts when 20k+ other people are applying. Is this going to damage my chances?