I’m going to disagree really strongly with you when you say, the broader the memeier.
A broad meme like handwashing is definitely a strong meme in the conventional sense; in the way Richard Dawkins, Susan Blackmore, and company analyze memes.
You could definitely write up a thesis on the cultural impact of “wash your hands” signs hung in places of work and how they have helped to improve public sanitation.
The problem is that it has little relevence to the subject of Internet culture.
I think we both agree that the broader the meme, the less relevence it has to Internet Culture. As you said, to treat these broad concepts as though they are Internet Memes is like saying they don’t exist outside of the Internet.
But, not every Internet Meme has to have original content as a source material in order for it to become an Internet Meme. The source material can definitely be from a mainstream event and still be an Internet Meme as long as the people have invented a new joke or new idea ABOUT that mainstream cultural unit that is recognized, shared, and propigated in online communities, in a context outside of general fandom.
We’re still not much closer to having a clear, concise definition of an Internet Meme though. We definitely need one. There are journalists who love to declare “OMG! THE NEXT BIG MEME!” as soon as they possibly can, after only a few photoshops have been made, before any genuine search interest has even occurred. I view this as being as low as inventing a news story for the ratings. A meme ought to be defined by genuine public interest, which is something that can only be measured after the fact.