In the end, I decided to buy the sets-Dora for Bailey, Hello Kitty for Sierra, and Toy Story for Blake. We made the deal, however, that they would have to take care of their own dishes, or I'd take them away. Sierra readily agreed. Bailey was a little more lukewarm to the idea of taking care of her stuff, but if it got her what she wanted. . . Blake, well, I didn't really expect him to wash his own.
Surprisingly, it turned out to be one of the better purchases I've made. In the past three weeks, our dish load has decreased by more then half. My kids, because they now know exactly who's cup is who's, only use one cup a day instead of three. Same goes for bowls and plates. We used to go through all of our cups and bowls in about two days. Now, we still have an almost full cupboard after three days with barely enough dishes to fill the dish washer. Very nice! And if my kids leave their stuff on the table, I know who to make clean it up. Oh, I help out a bit here and there, but even Blake cleans out his dishes as best he can. It's gotten to the point where I've decided to claim a cup, bowl, and plate of my own, and I'm even contemplating getting individual silverware sets for everyone as well (we go through spoons like mad).
I guess there's truth to the saying that sometime more is actually less.