Overall, I think you have a good direction. I would refrain from speaking negatively about your previous two schools, since this may convey the idea that you will never be satisfied with what you have and will always see the grass is greener on the other side.
Now, having said that, I think you should concentrate on the positive aspects that transferring would be to you, such as the research opportunities or the graduate programs.
If there is more that comes with attending a university on the tier of *NAME OF SCHOOL*, then I am ignorant to it and could only be all the more appreciative.
You could probably do away with this kind of statement. I see what you are getting at, but treat this essay like you would a job interview. You would never use the word ignorant about yourself in a job interview, and probably shouldn't here. Another way to phrase this idea would be:
"I know there are many more possibilities and benefits to attending *NAME OF SCHOOL* and I am excited to explore them all."
Or something like that. Again, play up how this transfer will benefit you in a way that your current school and your past school did not. Also, I think if you explain why you will finish your degree with *NAME OF SCHOOL* then you will allay concerns that you are just passing through without an idea of what you really want.
Hope some of this helps- I am a transfer applicant as well, so I understand where you are coming from in your essay. Good luck!