Professionally written. It's definitely worth a try.
If you higher a professional to write it in perfect handwriting, they have no way to know it's not you. Plus it will come across as super personal, and create an even stronger image of obvious effort. Showing dedication and the level of desire.
If a professional handwritten letter cost a lot, let us know, I (and hopefully a few others) will send a few bucks your way via pay pal.