First , lets go over the parameters : peace between house and the ncr
Main problems: arguements over the output of hoover dam
Main solutions : shared energy , supplies etc
Post other solutions
Parameter 2: Removing the legion
Main problem : kinda obvious ,
Main solutions: peace embargo (unlikely) , total assault (and push into arizona , if need be)*taking out the legion at the fort and through out the mojave could readily be accomplished by the courier and the house/ncr alliance if it succeeds, assuming it is established along the same lines as the four main questlines , before the battle a hoover, however a push into arizone could be a hard cause)
Post other solutions ,and parameters for success with solutions below