Should I retake SAT?

I took the SAT and ACT for the first time in December, with minimal preparation. I figured I’d see how it went.
On the ACT, I got 34.
On the SAT, I got 1560.

Obviously, I was ecstatic with my scores, but I realized I needed to retake one of them with the essay if I’d like to apply to Stanford and M.I.T.

When I retook the SAT in March, my score dropped to a 1530 and I got 17/24 on the essay, which wasn’t what I was hoping for.
I know I can do better on the essay, considering I poorly planned out my time on the essay, and I’m currently a straight A student in AP Language and Composition.

Is it worth retaking the SAT again in May for the essay?

Doesn’t Stanford require all your scores? In general it’s not a good idea to take a test more than twice. I’d either retake the ACT or not worry about it. Inclined to prefer the latter.

My son just got a 1530 on his first SAT and as far as I’m concerned he’s done. However, he didn’t sit the essay portion so if he wants to apply to an Ivy or Stanford he’ll need to do that. And he risks having a lower 2nd score (we were pleasantly surprised at this one tbh). Part of me just wants to encourage him to leave it and move on and not worry about some set of schools.

It’s tough to do much better than a 1560. I don’t think getting the extra 40 points left on the table is as good as use of time as getting more involved in extra curricular activities.

Thank you for the feedback! However, I wasn’t thinking of retaking the SAT because I want higher than a 1560, but rather because of my score on the essay portion.