I think it should be longer. I was told to talk a bit about yourself, your background, stuff that's NOT on your AMCAS or secondary. Then go into how you had a great experience at your interview and it made you more sure of wanting to be a part of the school and why you feel you make a good match for it. I talked about my interview in the letter, how it had really made the difference in showing me that the school truly cared about what students they accepted and wanted to know them. I talked some about how I liked the city and the location allowed me to stay close to home, which was a major plus. Then I basically said I would come there for sure if they took me. I closed with a thank you line like yours, pretty generic sounding, but I think a formal closing is appropriate in this case, I wouldn't do anything daring with the closing.
Good luck!