Highest Composite Score without Essay?

So I have taken the SAT three times.
Between the first and second I was diagnosed and treated for something that totally turned school around for me. My score increased by 160 points.
However, I was sick the second time, so I decided to take it again just to see if I would do better, but I didn’t take it with the essay, because I didn’t think my scores could go up by that much more.
I scored another 160 points higher, so obviously I want to send colleges these scores (and kind of need to since my GPA is split down the middle, and ended up super average). Most schools will take the essay score from one test and the composite score from the other, but I don’t think the UCs will.
Am I correct about this? Is there anything I can do? I don’t think that I have a chance at the UCs at all if I can’t submit my better scores. I have a 3.5 GPA (unweighted, my school doesn’t weight), and the good scores (in the 1500s) support my claim that I’m capable of doing the work, despite low scores early on.

Are they just unwilling to consider scores from SAT without Essay? Why is this? The essay isn’t factored into the overall score, so I don’t see why I should take it twice if my score was high the first time.

UC’s will only accept an SAT score with writing. They do not superscore and will take the highest score from a single sitting which has to include an essay.