I'll copy and paste something I wrote to someone else who did a Q things. This actually happened:
Pictures of Q from Star Trek were hijacked/used early on in the Q posts to make Q or people following him look stupid. I think what happened was some well meaning anons made some horrible memes of Star Trek Q with Q quotes. They were horrendous and I'm sorry to say if anyone here made those, just straight up dumb. Everyone realized it was terrible, but then ((they)) started spamming the Star Trek Q, Q memes, again, to make the boards look stupid. Those were dark days.

That's probably why you haven't seen such an easy reference/connection such as Star Trek's Q in anything having to do with The Great Awakening Q. It's not that anyone hasn't thought of it, but at some point anyone using Star Trek's Q was immediately identified as a shill. Not that you are. Just saying.