This is a suggestion after having thought more about my earlier ideas. I reread the part in "Silmarillion" on the rings and realized that the Elven rings could not be used in open combat but rather: "where they abode mirth also dwelt and all things were unstained by the grief of time." Translating this to the game is impossible, of course... But I thought of this:
Elven rings: The elven rings are individual, one for each of Elrond, Galadriel and Gandalf. Galadriel always accompanies Celeborn. If the respective leader/companion is eliminated the ring is removed as if used (i.e. the Shadow player may use it). This does not apply to the elimination of Gandalf the grey. In addition to it's use in the rules, a ring may be used to immediately add a card that was just played to the hand again. This applies to the following cards only:
Elrond: "Wisdom of Elrond", "A power too great" Galadriel: "Mirror of Galadriel", "A power too great" Gandalf: "Wizard's staff", "A power too great"
The Shadow player can only eliminate Gandalf the White by the use of an event card as a battle card if an Elven ring is also used and the Witch King is present. An Elven ring may be used to discard the card "A power too great" if the Witch King is with an army adjacent to Grey Havens, Rivendell or Lorien.
The Witch King may only be eliminated by the card "Fatal strike" in either of these cases : 1) Eowyn is present. (Eowyn is the last Rohan leader to be mustered. ) 2) A bearer of an Elven ring is present, and that ring is used when the card is played.
(I have made my house rule less radical, while still trying to add more weight to certain characters that are tied to the fate of Middle Earth. Gandalf and the Witch King can still be killed when their army is lost, signifying a fatal loss to their cause rather than being killed "normally".)