After spending an hour or two learning the rules of Caravan and then rinsing No-Bark Noonan of all his caps, I got the Win 3 and 30 Games of Caravan achievements. That left me with 4 achievements – one for getting banned from all the casinos on the strip, one for completing the game in Hardcore Mode, and the remaining two for the two final NCR quests.
So, after almost 100 hours total play, I finally completed New Vegas the way I intended to in the first place. Hurrah!
Now, about those other two achievements…