Your question is a good one. I'm going to weigh in here and give a lawyer's view. In my opinion, the instructions are ambiguous. They define four different limits that can be read to interrelate in different ways: "at least 250 words," "(3000 characters max)," "but should not exceed the space provided," and "250 to 300 words." Construing the limits together, one could adopt a conservative interpretation, i.e., that the essay MUST comprise at least 250 words but not more than 300 words, and in no event more than 3000 characters. Alternatively, one could adopt a liberal interpretation, i.e., at least 250 words (and typically not more than 300 words) but in no event more than 3000 characters.
A compelling argument can be made that the spirit behind the limits is intended to encourage applicants to write concisely, simply, and directly--not to reward them for using exactly 250-300 words. Why should one applicant be penalized for writing an essay of, say, 380 short, muscular words totaling only1600 characters that falls far short of exceeding the space provided, and another applicant be rewarded for writing an essay of EXACTLY 300 words of purple prose and 3000 characters that completely fills up the space provided?
I'm not trying to pick a fight or stir up trouble. I'm just pointing out that the instructions are subject to more than one reasonable interpretation. That said, the wisest and safest thing to do would be to adopt and follow the more conservative interpretation.