For the cylindrical map, I selected my object, then went create UVs > cylindrical mapping. It's set to w/e the default is for that. I then rotated the map around until it was on the correct side.
As for using the texture reference, I apologize in advance since I'm not that great with Maya, but I clicked on my object (which when I do, selects the sycloth1shapeTrf), and hit create texture reference object. It created the reference of the selected object, but I feel like I'm supposed to do something with that reference, because when I hit play, nothing has changed. ![]()