But if The One Ring has been acquired in result of influence attempt or CvCC at Mount Doom, a moving company back and forth does not make (thematic) sense.
In past I have not treated the text as rule, but as description. Similarly to:
Lidless Eye wrote:Any gold ring in one of your companies at Barad-dûr at the start of the end-of-turn phase is automatically tested. Any ring test at Barad-dûr has a -3 modification.
If you store a gold ring, it is automatically tested with a modification of -2.
If to treat the text as rule then any gold ring test at minion Barad-dûr would be modified by -6 (-3 by rule, -3 by Barad-dûr text).
Gold rings stored at Carn Dûm would be tested with modifier - 4 (-2 by rule, -2 by Carn Dûm's text).
Texts of Cracks of Doom and Gollum's Fate do not check for history of The One Ring.
If problem is that it makes The Precious, The Will of the Ring, The Ring Will Have But One Master less usable then a proper way to address the problem is creating an errata to Cracks of Doom and Gollum's Fate.
Namely replacing the first occurrence of "The One Ring" by "The One Ring moved here by your company" in texts of both cards.