Thanks Steve. There's nothing inherently wrong with fairway going around the green. You just have to make sure the lines don't intersect/touch and that you combine them into a multipolygon. For instance, if you look at https://www.openstreetmap.org/way/1352433807, you can see it has great imagery and the fairway grass can be seen going all the way around the green. In that case, draw the fairway all the way around, select both (shift click them) and then type 'C' to "Merge" them together into a multipolygon.
