There is more to Phase III than just elevating the litter box, the final step is to place the litter box on the seat. I forgot that bit until I read the instructions again. The litter box has been on the toilet (with the seat up, it was sliding off otherwise) since Monday night. They didn't even blink an eye and are happily using the box.
That just means they had some more time to get used to the high litter box. It's better to take things slow, than to clean the consequences of going too fast. I'm not sure that I want to start the next phase this week anyway because I have a business trip coming up and I want to be home until the last, crucial bit of the training is finished.
I doubt they'll learn in less than a week how to use the toilet and I don't want to force them to learn too fast. The downside is that there is litter all over the bathroom floor. Having the box without a lid means that if a kitten scrapes a little too vigorously, there's litter flying everywhere.
Oh well, this too shall pass. I'll just swipe up the litter regularly for the rest of this week and begin with the next phase next week.