What happens to my essay score if I don't finish in time?

I got through the intro, and about 1 3/4 body paragraphs of my essay (I was planning on having 2 body paragraphs and a conclusion). I've never been a very fast writer, but I've always been a good one. I definitely believe that the quality was good, but what can I expect if the quantity just wasn't there (it was a bit over 1 1/2 pages)? Do you have any advice to help me complete an essay in the allotted time if I take the SAT again?

If the quality of your essay is solid besides the fact that you didn't quite finish it, you shouldn't expect to lose too many points. The new SAT essay is graded based on three criteria, each scored from 1-4 by two essay graders to make up a maximum score of 24. The three categories are Reading, Analysis, and Writing. Based on what you've said about your essay, you would probably score a 2 on the Writing component from both graders. One of the qualifications for a score of 2 is "The response may include an ineffective introduction and/or conclusion." Responses that score a 3 on the Writing component must "[include] an effective introduction and conclusion."

Since you say that you're confident about the quality of the essay in general, you would probably still get 3s and 4s from the graders on Reading and Analysis. My estimate of your final score is around an 18-20 if your representation of your essay is accurate. You can read more about the scoring criteria in this article.

My advice for improving your time management is to complete a few (timed) practice essays before you take your next test. You'll get a feel for how much you can write in the allotted time and become more accustomed to the fast pace of the section. Also, sometimes it's easier to write faster if you plan out everything you're going to say ahead of time and stick to your outline. You'll end up writing a more organized essay and avoid stretching out the length unnecessarily.