I have tried suspending sweet potatoes in water with toothpicks. It worked OK, but I was not impressed. It was lengthy and the water needs frequent changing. This year, I am doing the soil method in a cold frame. I am loving it so far! We will see what happens in a few weeks.
My cold frame is an old sandbox my children played in for many years with repurposed window panes on top of it. It's not very pretty, but it was free and was very simple to make.