None of the OP's plan would ever work because of the endemic problems in the NCR to begin with. Kimball and Oliver got into power because they're of the prevailing mentality in the NCR currently: Hawkish Imperialistic Jingoism.
That's why the NCR needs its nose bloodied. Kimball needs to survive his boneheaded PR stunt (to keep him from becoming a martyr and to personify the folly of hawkism), Oliver needs to die (to put the fear of death back into the hawks in the NCR), and the NCR needs to GET OUT.
House, or better yet Indie, is probably the best ending for the NCR in the long run. Covering for Hanlon also helps too, as he gets fed up with it in the epilogue and rides a wave of disapproval of Kimballs way all the way to the Redding senate seat.
The only endemic problem is with as you said Kim and Oliver. They're bad leaders, bad managers, bad officals, and that shows through their stragety. But just because the leaders are ineffective doesn't mean the system is per say. The NCR doesn't NEED to lose they NEED to change stragety.
To everyone talking about the Fiends.
Listenthe fiends are A problem but they aren't THE NCR's problem. When dealing with the Legion they need every troop from Mccaran down I-15 securing for safe passage, taking on the BOS/signing a peace treaty, killing Tabith and setting up a pirate radio station. And this speaks to Helios One also, they have a limited number of resources, a limited amount of troops and could use them on more productive things. Remember how the quarry is key to foritifing bases? Or how the railroad along I-15 is key to rapid deployment? Or how Primm is the second largest city in the game and a major tourist trap? Those are more important than an ineffective base south of Vegas. And I would argue that's its not even the policy that's the reaosn they can't handle the Fiends, it's because the Fiend's are good emenies.
Go to youtube and watch some endings where the NCR goes against the Fiends. EVEN though Mccaran is their largest base, EVEN though the fiends have no intellegence networks in the base, EVEN though it's arguably the most heavlily fortified base they have, EVEN though they have power armored troops, they STILL lose massive numbers of troops. So why not send those troops to dealing with I-15 instead of trying to secure outer vegas. And even IF the NCR did bring down the fiends, now what? Westside still hates they don't have enough troops for security, the NCR squatters are still coming, Freeside is under King control and they hold general contempt for them anyway.
What's the best way to gain support from the Vegas population? Show them how weak they are WITHOUT the NCR. Show them what happens when you don't have the troops there, when you don't have Big Daddy Two headed bear. While at the same time you've secured Goodsprings, Primm, and Nipton and have boosted the economy. By the time the BOS is done, the railroad is finsished, Tabith is gone, and I-15 is secure, you'll be in a much better position to Annex Outer Vegas communities.
I'm sorry I have to say one more thing about Helios One.
A. All the troops at Helios one could be more effectively used securing Novac
B. Used in keeping Highway 93 free from raiders, and mutants. Remember Golf, Forlorn, Hoover Dam? All are mainly supplied by 93.
C. Take back Nelson reinforce the offensive campign
Besides that there are risk with the place
A. You need at least Rangers to clear out the basemant to operate it. Mind you they could be doing more productive things like taking on the BOS, or Tabith, or Cottonwood etc. It's an unnecceracy risk
B. After it's up and running there's only one specialist to run it and he's not going to actitave the weapons systems
C. The Legion want it, the BOS want it and with no troops in Novac it gets even easier for a raiding party
So why not just scavenge the place? It's not worth it. Highway 93 and Nelson are more important.