@Edisonian . . . you’re almost the perfect reason why the UCs should allow mixing and matching of SAT M & EBRW with essay scores because even if the essay does minutely factor into the ACT score by component (but not the composite), for the SAT, the essay has zero input into one’s composite or component scores.
And if a student scores 24 on the essay on his/her first take of the SAT, then why would this student want to retake the essay if he/she wanted to score higher on the M & EBRW?
But rules are rules. The UCs mainly want to see effort in one persevering through three hours of the two sections to get to the ~ one-hour essay. And by taking the essay at all sittings, it can only improve one’s writing and standardized test-taking, irrespective of what you manifested in your two takes of the essay.
I would contact UC Admissions to see if there is another way around the problem. Surely the 1,370 score is more important, and by reporting its 17 score on the essay, the UCs will also note that you scored 22 on the essay in your first take by sending in that score (edit: besides the fact that UC wants full disclosure anyway – they want all scores sent in). They’ll also note the increase in M & EBRW in your subsequent take and give you points for their increase.