I left the below comment about essays here today. It made me think that perhaps I can use some of my own advice, seeing I'm in the final stretch, working on my last set of essays.
Few things - first, I'm by no means an expert. I have been fortunate enough to get past the "mess" stage and submit a few applications. That being said, here are a couple of suggestions based on your post.
First, if you need to rewrite - go for it. The hardest part of the essays, imo, is the content. Once you get the content, you can fix the transitions. So figure out what you want to write, what makes you special.
Second, get a first draft complete. Yes, it won't be perfect, but when it's YOUR writing, sometimes it's hard to see the big or outside picture. Find a close friend that is good at editing and let them review it. (Two ways to review, just give it to them and let them tell you what they think or specifically ask them if you have answered the question and mark up syntax errors/grammar/spelling, etc.) In addition, another way to personally review your essay, esp. essays with word limits, read each sentence, make sure it relates to the question, then if it does, see if it's necessary and important. You'll be more concise.
Finally - remember, this is a process. And sometimes it's easier to leave an essay and come back to it later.
One last minute addition - from a very wise admissions guy named Jett. First draft - drink a beer, glass of wine, or even tea and just write. You can fix it later, but put words on the paper. Second, make sure you are writing about YOU, not what you THINK the adcom wants to hear. If a question asks about YOUR definition - don't google everyone else's because that is what the rest of the prospective students will do. Literally, define it in YOUR words.