The best route is Jean Sky Diving -> discover Hidden Valley. Fast travel to Hidden Valley, turn right, run through the gap in the fence towards Black Mountain. Ignore the 2 scorpions and the centaurs, they are idiots and won't successfully connect an attack. At the centaur camp, hog the left wall which leads to a ledge you can use to jump the Black Mountain fence.
Hug the right side once you jumped and continue upwards the mountain until you discover the location. Immediately fast travel to Black Mountain. turn around and walk straight North. You will hit REPCONN HQ and you can choose to go to the 188 for Veronica or take the Eastern road North to Vegas (along the Grub n Gulp).
I did it on my first playthrough (which I understand was really weird). I started Lonesome Road at level 2, and then spent pretty much all the ammo I got taking out the Deathclaws (and even then it took multiple attempts).
I apparently did the DLC in reverse order (starting with Lonesome Road, then Blue Mountain Blues, and then the Sierra Madre), and never met a Ghoul until after finishing the game and backtracking with an older save.
I just ran. Nothing more to it. Didn't stop until I was close to The Strip. Made the game a lot funnier to me to get encounters that you'd typically get earlier on very late.
With a high Luck/sneak and a stealth boy, it's not impossible, after fifty tries, to just sneak through the thin net of death claws and just walk to Vegas
Second play I headed due north of Good Springs all the way to the Great Khans, keeping as far distance from the doom flies as possible, I think one or two chased I didn't stop to look.
I was being colloquial with "sprint". You can get past quarry junction on vanilla by relying on areas where small rocks disrupt deathclaw path finding and get them confused.