There are multiple throws in historic literature labeled as Cross-Buttock. Without exception they are all some form of trip or hip-toss which pulls or draws the person being thrown (Uke in Japanese parlance) across the hip of the thrower. Sometimes it was sort of o goshi/koshi garuma type throw, lifting the opponent up on the back. Sometimes it was nearly a tai otoshi.
It may seem stupid, but before the advent of Marquis of Queenberry rules, there was no ban on wrestling. In particular, I have heard of a "cross buttock" throw ( very similar to the koshi-guruma in Judo).