All this to be a prefect xD, it's only worth being a prefect (or monitor) at a large independent school like Harrow or Eton. Other than that, I don't see the excessiveness of seriousness in the application process in other schools. Being a prefect is a responsibilit to represent the values of your school, I was headboy at my previous school, before moving onto sixthform. The process was a simple letter to the the teacher responsible for prefects, accordingly my place was automatically chosen by the senior members of staff. The appointment of headboy was immediate, without any vote from the school community.
You need to understand, that you'd probably become prefect without a speech, the votes from the teachers matter the most. The student body generally express preference to their friends, and thus becoming a popularity contest. Popularity contests are inherently flawed and do not favour students with academic or extra-curricular ability, these contests could therefore be exploited with entire friend groups being chosen or selected as becoming prefects. Therefore, there is a boundary to the power of a student vote, the teachers provide this boundary. I reccommend that in order to see confidence in yourself, consider what you have contributed to the school community, what activities and responsibilties you have committed; and most importantly your academic achievements.This is probably becoming a rant about student voting, but you need to aim to impress the teachers ; so don't worry about the impeccability of your speech.
Your speech seems to be "original" for the standard speeches, however similar originality with starting speeches with a comedic anecdote is becoming regular. Although, the impact of the opening is fine. There really isn't much critique about your speech, and if there were to be votes alone, then you'd become prefect. Comedy is critically important when appealing to the student body, they need a personality to intereact with.However, it is important to say "what you can bring to the school", don't be cliche and say the boring "emotional contributions or producitvity to the table"; actually suggest something that can develop the school. Upon leaving my inadequate rated community college, it became an academy, adopting all the long list of suggestions I left, (inspired by Harrow School). Recently visiting my old school, during my holidays, it was good to see my adapatations were installed across the school community, with more elitist rankings and status, differing the average student from the academically talented ones. With more "Badges" and resposibiities to become leaders.
Your key is to impress the teachers. Teachers know what friends groups are, they can see through students who "Purposely" and try working their way up to become prefect or head prefect, it's evident in every school. But you'll know who these people are, the ones who try insanely hard to "PLay the ball", never succeed. Always expect the unexpected, as we are in times of change; anyone can become prefect or head prefect if they make an inspirng speech and target the key teachers.
Good luck,