Does this have a name?

It's context-dependent and might not even be a fallacy (could just be plain old deception).

Assuming it is fallacious, what did come to mind straight away is hypnotic bait and switch. Sounding off a bunch of things the audience can reflexively agree/disagree with, then presenting something unrelated as the solution to those things.

I'm not clear on the context – it seems that the situation involves 11 statements, 10 of which are accepted as true (or perhaps are actually true) and one (perhaps the last one) that is actually false but there's a hope that others might believe it to be true.

It doesn't seem like an argument, to me ... just a series of statements.  If that's the case, it wouldn't be a logical fallacy – just a false statement made in hopes that others might believe it.

I can't see any argumentation, let alone any invalid argumentation or errors in reasoning that we'd need to call it a "logical fallacy".  Rather than bad logic or reasoning, what I see is bad (or false) information. It strikes me as a "fallacy" in the sense that it seems to be an attempt to deceive or trick but the fallacy comes from the untruth of one or more statements, not from poor logic or reasoning.