Think about a compromise. Write up a draft letter, then visit him during office hours with a copy of the letter. Go over the points that you covered in the letter, and why. You can also express your concern about the voice of the letter being your own. I'm sure he'd be happy to work with you, while being appreciative that you did the bulk of the work of letter writing.
Hey pwu103, I'm trying to access the document, and I can't seem to get to it. Are you sure it's posted correctly? If you get it back up, I'll gladly give you technical and content edits. Cheers!