I managed to figure out a solution, so I thought I’d update the post in case anyone else is looking to do something similar.
Take the layer with the 3D stroke and set it’s Z-depth to = the radius of the sphere in the Orb plugin.
That gets you close.
Make the masks in the stroke layer, with one end always starting on the centre of the layer so that when you apply transforms in the plugin at least one point is in the right place.
Use transforms within 3D stroke to find the correct orientation for your paths. You can adjust the paths themselves, but you’ll only really be able to control the length of the line that way.
Using a camera orbit to check the contact on the limb of the sphere works well too.
Thats it.
Hope it helps someone else.
Markus