Actually, the way it works on the Magic is that when you enter Palo for reservations, you're in the dinner reservation line. While you're in this line, they'll give you the aforementioned slip of paper, which you can fill out while waiting in line. When you get to the head of the line, they'll collect your slip and then you can proceed to the brunch table, and then on to the high tea table. The process is not nearly as tedious as it sounds. On our last cruise, in December, I think I made dinner and brunch reservations in less than 10 minutes, and there were maybe two people in the "high tea" line when I finished.
You can avoid having any of these on the same day pretty easily. For example, say you want to have dinner on Tuesday night, brunch on Monday morning, and high tea on Thursday. For your three dinner choices, list "Tues 7:30," "Tues 7:45," and "Tues 8:00". Then just schedule brunch and Tea on other days.
There are far more dinner spots on the 7-night trip, so you can usually at least get the night you want. I've always gotten my first choice for time, too. If you arrive for reservations shortly before the scheduled time, you should have no problem getting what you want.