First not all resorts have a "dedicated" room assigner, as Floridacat stated, the Deluxe resorts do, but the moderates tend not to (they still have someone assigning rooms, but that is after all the other operational support work is done.)
As for the fax itself, keep it short and sweet. Make sure you put your requests in the order of importance that way if they can not fill all of them they at least know which to try hardest for. You can write a little telling them why, I personally love the stories about Little Johnny's first trip to Disney or on our honeymoon we had room Whatever and would like it again. Just don't make it a book.
Also keep in mind the best time to fax (or call) is between 5pm and 10pm. The morning room assigner is overwhelmed with check outs and check ins and usually does not have time to even take a break. The night time room assigner is usually really busy up until 4pm (when all the rooms should be clean and ready) after that they are usually just working on blocking rooms for the next 3 days. With that said remember that the reservations are held in the CRO/WDTC reservation system until about 5 days prior to arrival and the rooms are usually not blocked for requests until 3 days so don't fax to early (it may get lost). Also if you decide to call most resorts now have one central phone center (that is usually answering the calls for 3-4 different resorts) that is not at the resort itself. So unless you know the direct line from previous vists or someone on the boards, you probably are talking to someone that is not even at the hotel.