If understanding and breaking the Limit of the Lunar Sphere is needed, I would suggest studying and Armillary Sphere, its mechanism and its enchantment. Amongst other, it has "Know the Heavens" and "Track the Heavens", both InVi which are able to sense the astrological time and the influence of the planets. To me, it sounds as close as you can get from probing the Lunar Sphere (The Mysteries, Revised ed, p 53).
Studying and exploring area with strong astrological connection, like Stonehenge could also give insights. Maybe also some observatory in Levant Tribunal, in Persia. Possibly even getting some documents from the Mythic Cathay (and of course being able to decipher them).
Finally, getting to the Purple Islands could also lead to some significant Insight, after all, if they are the reference point for the Geographyca from Ptolemée, there must be some strong connection with the star and the Axis Mundi.