You need to realize that perfection has an asymptotic relationship - you can spend forever trying to make your essay just perfect, but you'll never quite reach it.
That said, do not agonize *too much* over the essay. Yes, it is very important, but the simple truth is that after so much time and after giving it your all, it's simply time to submit it and move on. And once you do happen to submit, do not think back on it and don't get caught up in regret.
As for your dilemma about how to structure it, can't you do a thesis type statement AND a story both at once? This seems possible and it would be good 😀
Anyway, there's no dire / urgent push for you to submit just yet, so take it easy and submit once you feel comfortable. If you are still uncomfortable, that's okay; there's no pressure at this point in the game. You can still submit AMCAS in july and be quite early in the application game. Remember that SDN'ers are very hard-core and people here literally fill out the whole application on or before June 1!!! This is not normal behaviour. So don't get intimidated when you read how everyone here is submitting, or about to submit, and how early we are, or is it too late, etc. It's just rubbish 😀
Good luck with the PS! 🙂