This is a topic that I've gone over a lot in my mind.
Firstly, the easiest way to get people interested in sixes is NOT to make them play it, it's to show them something relating to sixes - to show them what TF2 can be when it's played in the 6v6 style.
I don't know how much things have changed, but back in the day when all I did, in relation to tf2, was pub, I was at least loosely aware of who TLR was, and B4nny - I imagine the profiles of certain Invite players' names has increased due to highlander and the wide swath of the community that knows people who have or are playing HL.
The best thing we can do is to advertise - a bit like Kissme said, but there are other ways than going in public servers with a # name, especially since I doubt many people actually go to websites they see in hashtags, and I imagine some server populations would be pretty turned off by somebody having an advert bind or at least be suspicious of it.
Like I've said in the past - the best thing to do is for somebody officially associated with tf.tv to reach out to pub communities and get them to advertise tf.tv or if they're really active, the MOTW directly to their communities. Obviously trying to get Valve to give us a hand would be nice too - but I doubt that'll happen.
Then we just have to have a good stream set up and we're gold.
Frag videos are helpful too, folks really need to start dropping adverts in their frag videos, because oodles of people watch frag videos.
People who have no innate interest in 6s aren't going to go out of their way to struggle with all the crappiness that comes with starting out, we have to hook them on the comp scene by making them aware of the products tf.tv provides, and in turn turning out quality products. Then an extremely small portion of those individuals will actually try out sixes and intend to stick with it for a long period of time.