@clacke The rhyme came after my time, I think, because my teachers all used the problematic phrase "Indian-style" to describe that way of sitting.
That said, "criss cross applesauce" was a common phrase in patty-cake games when I was a kid, and it very much rhymes in my head. I'm trying to imagine how to pronounce it so it doesn't rhyme and I can't even imagine it.