How can I lower my "Templar Awareness" quicker?

Solution 1:

You can't really lower it any faster than just looking for notoriety lowering people whenever they show up (as you've noticed, there's only heralds and witnesses). It's more the fact that it works differently than notoriety in AC2/BH

Guards no longer care what your notoriety is (at least as far as I can tell) even when you're in the red.

The red seems to be meaningless except for one detail. As long as you're in the red, doing something that would raise your notoriety has a chance for one of your dens to come under attack, with more notorious things (like buying property) having a very high chance.

The idea is that once you hit the red, just don't buy anything or kill anyone until you've managed to become secret again, and you won't have to worry about ever being attacked again.

If you manage to get all of your dens a master assassin, then it won't matter if you're in the red as none of your dens can be attacked (I'm currently at 6/7 dens locked, so I'm not sure if this is true, but I'm guessing either it won't matter anymore, or your notoriety will be locked at 0 or something).