Most cults limit their interaction with the Hero Plane to worship and other such ceremonies. The God Time is brought close, priests and initiates communicate with the Divine, draw upon the magic of the God Time, and stick to what is known and traditional. Since the end of the Second Age, this has been norm.
Very few cults encourage active exploration and experimentation. One of those is Orlanth, whose possession of the Mastery Rune denotes heroism more than command. The Orlanth cult cannot help but explore and interact with the unknown – that after all is the way of their god.
Another exception was the Tournament of the Masters of Luck and Death which was an ongoing experimental quest, although limited to the powers of the Holy Country. The Red Goddess, as well, encourages her initiates to find their own spiritual path, for better or for worse.
As an aside, few ruler cults have the Mastery Rune. So far I believe Orlanth is the only cult out of more than a hundred with it.