Having used that method on smaller globes, I can tell you it's a nightmare to keep level. Unless you are an octopus. And I don't think Rob is.....
Assuming that the central pole-to-pole axis is perfectly vertical, you might want to consider making a large surface gauge. Something that can be adjusted to whatever height you need and is rigid. That way, you can place the base of the surface gauge on the same surface that the DS is mounted to and "draw" it around the globe. So long as the surface gauge doesn't change position, the line should be perfect.
Gene