The way I did was to stealth kill every NCR soldier up until Cottonwood... Just make sure you save the dog tags. Also make sure the game counts it as a stealth kill. It can be time consuming, but I found it fun, and was able to kill everyone in that outpost with the sniper Ghost on the building that was not in the bar. Also remember to pack at least 1 set of NCR armor...
The only real problem is when you get to the Strip. You will have to wear NCR faction while in the Strip or else they will attack, and the guard bots auto help the NCR

. You will also have to remember to take off your NCR armor before fast traveling back to Caesar... I died so many times due to this.
Its true I had less XP from turning in quests, but the extra kills the NCR/Powdergangers/fiends/kings/boomers/khans/BoS/those silver rush folks netted me more then made up for it... man the Legion sure had a lot of enemies before I joined 'em.
TIP
After turning in a crap ton of dog tags to the Phoenix in Cottonwood, and getting your rep up... kill him. If you wait for him to go in the building you can stealth kill him, and gank his epic armor, and weapon. I RPed it as meeting the man, and finding him weak, killing him, and taking his stuff/job because I could do it better not being stuck behind a desk. Caesar would have wanted it that way

.