Looked up sources from Peter Taylor's link and in my mind, Snowclones is the correct term for these new meme-clichés or rhetorical tropes (since both these terms fall short; many of the now modified original quotes weren't memes, or at least they don't have to be. They might become memes from snowcloning them, ie. "catch on", but this is after the fact. This also means that you must agree with that they don't have to already be in popular culture, as mentioned by Daniel. Again, they might become part of pop culture. Their use may be rhetorical, but it's not a property of them. Trope doesn't describe this new phenomenon distinctly.)
Snowcloning is the process.
If you're afraid terming them Snowclones is confusing, you will just have to write it out more logically as "modified catch-phrase" or something like that.
It's one form of reference humor, where the speaker counts on the audience having heard a quote, seen a film, or similar.