I think the canonical ending will have to be a stalemated conflict, with both NCR and Legion retreating after both realize how overextended they are and unready for an all-out war (despite what Caesar thinks, his primary strategist was pretty willing to concede that point and go home without a serious fight in the independent ending).
That leaves House "in-charge", which doesn't require much fudging in story detail to include both House and yourself as co-rulers of a shaky New Vegas, something along the lines of:
"Although he achieved the independent New Vegas he dreamed of, House didn't survive to see its zenith, dying mysteriously in the aftermath of the battle, his trusted lieutenant, Courier Six, ably stepping up to run his varied interests after showing a deft hand at manipulating the local powers..."
Something like that, vague enough about House so that he could have died of Legion/NCR vengeance after the battle, or been killed by the PC before/during it, or just succumbed to 216 years of pickling in a spicy dill-brine mechano-casket.