Well, I got screwed by the (glitchy) system.
So, I logged on to my account at the 27-day mark to the start of my trip (last Sunday for October 16th start) and used the 12-digit booking number (room only). Well, the dates on my account showed September 27th-October 3rd.
This was the dates I had a trip booked, but canceled that trip many months ago, before I even booked my original trip. It was under a different reservation number, so it seems the system has a glitch there.
Well, since I actually received the e-mail invite, I tried calling Disney, even though there is no help desk number. After talking to several CM in different departments, they finally transferred me to IT. The person seemed like they were going to be helpful, but it doesn't seem like they ever did anything.
My guess was that when that first bookings dates ran out, the dates would reset and I would be able to book for our trip. I was right - today the dates now show the correct dates, October 16th - 20th. Well, guess what, all the dates are full already.
Truthfully, I am just slightly annoyed. I know this system is not very good. People are booking that aren't invited, and I would've tried to be one of those people, so I can't get mad for other people doing that. And in the end, we've eaten there once already (for dinner), it's just the DW and I this trip and we don't really care that much.
Just warning people - if you move your dates, you create a different log-in to try to access this website or else it will override the correct dates with the wrong dates.