I'm with Tatgal818; just do it! I cannot guarantee that you will get everything you want, but I can just about guarantee that you'll have a great time.
Things to know: Palo has other meals besides dinner. They do brunch, and sometimes tea. They continue to book even on the ship; both the first day and also throughout. On our last cruise we got some good news in the morning which I wanted to celebrate. I visited Palo and yup, they got us in for dinner. In fact, until this October cruise, I have NEVER prebooked Palo. (I did this time because I will be Platinum and my Palo visit will be free!) Here're two Palo tips: the first is that many people do not want to go to Palo on the first night. The first night is the one where you meet your table mates and your server and there's no guarantee that your clothes will be delivered to your stateroom in time. Thus, the first night usually has more availability. (In fact, Disney recognizes this and on longer cruises has begun to allow a second dinner in Palo for those who book the first night. The second tip is that Pirate's night, although it has its adherents; that is, some people prefer to go to Palo for PN and time dinner to watch the fireworks, many other people do not want to miss PN, so you might find availability there.
I won't say that PA never sell out. They do. Usually, frankly, due to limitations on behalf of the subcontracting tour company. Last May's EBTA sold out of Stonehenge tours, notwithstanding the fact that something like 80% of the ship were booked on them. But for other tours you've got to remember that we don't all want to do the same thing. You might be dying to go on an Anne of Green Gables tour, but I have no interest. People have up to three days before sailing to cancel their PA without charge, so check during that time period to see what has opened up. Meanwhile, yes, people change plans all the time, switch PAs, cancel and decide to take it easy, cancel and decide to do private. Also, sadly, some people cancel the entire trip. So yeah, things open and change all the time. Also, the cruise line works with the subcontractor and they try to provide what people want. If more people book trip A than B, the subcontractor switches some of his "B" buses to the "A" trip. Another thing that happened to me was this: the website showed "sold out" but the truth was that the tour company didn't run that particular trip. Sometimes things depend upon Mother Nature and she doesn't cooperate.