House rules to fix LotR Risk endgame
I find that when considering house rules, its best to think about why something is happening and attack the cause of the behavior.

The root problem as I see it, is that once the ring is one die roll away from destruction the game has a 50% chance of ending before the current player can lose any newly acquired gains.  Conversely, any reserves not spent that turn are increasingly unlikely to be used productively for each additional player in the game.

Consider adding one last "round" of play after the ring would be destroyed at Mt. Doom.  Essentially, when the player who "destroyed" the ring finishes his next turn the game ends.

By adding an extra round, you remove the random element of the game ending, allowing everyone to plan ahead and try and defend their territory rationally.