The Swan and Dolphin are convention hotels and actually do very little Disney business. Most conferences are reserved from 2 to 5 years in advance (I know, I chair the site selection committee for a national organization and we are currently looking at locations for 2007 through 2010!). About six months before the conference, attendees begin making their reservations. About four to five months before the conference, most attendees have made their commitments to attend...paid their registration fees and the conference organizers have an idea how many rooms they will need for their conference. They will begin canceling excess rooms in their blocks so the conference won't be responsible for paying for the unused rooms.
You might start calling 4 to 6 months before your trip, or you might try this strategy. I have reserved a room at the Dolphin in July for the week between Christmas and New Years and got the gov't rate. This is because this week, the week of Thanksgiving, and the week of July 4th are the least likely weeks to have conferences because of the holidays.
However, bear in mind that the week we were at the Dolphin between Christmas and New Years was also the week that a Japaneese tour group checked into the Dolphin and, according to the bellman that took our bags to our room, had checked into over 1,000 rooms at the Dolphin. So it may be a holiday for us, but a great time for non-Christian nations to get a great deal on unused hotel rooms and see our beautiful Christmas decorations. Same might be true for foreign guest the week of July 4th.
