Frankly, to condense the grounds on which you are appealing into a short 250 word "essay" is unreasonable on the part of the university. My personal grievance against the word limit aside, I encourage you, with the fullest conviction, to firstly pen a full-lengthed essay on the merits of your achievements, point by point refutation of any misgivings which may be formed in the mind of an admissions officer pertaining to your suitability for university academics, and the career aspirations which have advised your selection of that particular course you are appealing into.
Secondly, summarise these points into a 250 word "essay" as per the appeal requirements. A piece of 250 words can only be said to be a summary and an un-wholesome representation of the candidate. If an admissions officer was to be truly invested in the task of scouting the most exemplary candidates, they would not merely settle for such an insubstantial document. This leads to my third and final point: submit the full-lengthed essay you have before written via the appending of it on an email directed to the admissions office, taking great care to iron out any kinks in grammar, sentence structure, syntax, and any other element of your essay you have deemed necessary to include. I speak from experience that the word limit is of no significance in the decisions of the admissions officers; whatever has been printed out by the admissions office for their perusal WILL be read by them. I flatter myself by saying that my appeal essay, which far exceeded the word limit, not only granted me entry into my desired course, but also a full scholarship. Granted, the interview played a crucial part but my instincts attribute the success of my appeal to my essay.
In fine, disregard the word limit. It is but a weak mechanism for the weeding out of the unmotivated and therefore unsuitable candidates. Let not such a triviality be the impediment to your future, your success, and your career choice. Do everything in your power to secure the course you most desire.
Sent from my bowels to your mouth using GAGT