I disagree that a letter helps an applicant look more professional. Perhaps that was once the case, but with admissions offices being so busy, I think email is less likely to be lost.
I found the opposite to be true at the school I requested additional funds from. I initially submitted an informal e-mail to the school and never recieved a response. I then went snail mail and received my additional funds a week later. Either wasy is fine, I do however, believe that drafting a letter on nice paper and with a nice letter head places the idea of legitimacy in the reader's head (Not all readers). I majored in psychology for a quarter so I know how people think
Your suggestion for attaching other offers from additional schools is excellent.
To the OP: Just remember that everything in life is negotiable. You are walking into a car dealership. These people want your business...let them earn it!