A current fad involves "treasure hunting" for small free things. You use a map, find a gps coordinate, or follow clues. At the end, you find a small "prize", usually a toy, piece of jewelry, a coin, or tiny art. Finders will often post online photos of their found "treasure". Why not stuff their treasure chest with items that say "Q"?
https://www.pokemongo.com/
https://www.geocaching.com/play
https://www.parentmap.com/article/painted-rocks-treasure-hunt-kid-craze
https://en.wikipedia.org/wiki/Treasure_hunt_(game)
All these treasure hunt games were created in the last few years. Is there a talented social media geek that could start our own "Find Q" treasure hunt movement, based loosely on "I Spy"? Create a Facebook page or website for people to post that they have spotted a "Q" with a location and photo included.The guys at the Trump rally, and the Atlanta billboard (the first Q billboard?) get the first posts.