Attempting to rescue logical positivism

Logical Positivism didn't fall because people asked if the verification principle is verifiable; most LPists were clear that the verification principle was supposed to be analytic (it's somewhat murky what that means, but for present purposes it should suffice to note that in any version it amounts to something similar to what you suggest here). This version of history is even worse than the story that LPism failed because of the impossibility of drawing the analytic/synthetic distinction; at least that criticism was actually made, and believed by some, though it also fails to explain the disappearance of LPism as there still seem to be large numbers of philosophers who believe in analyticity or something like it. Why none of the believers in analyticity call themselves Logical Positivists any more is a complicated question, and while there are some substantial issues involved, some of it seems to involve something more like a change of fashions.

"No, that's not a belief, that's a definition of what it means to say 'I believe X'."

That's not a definition, it's an act of linguistic warfare.

If you were actually defining a word, you could replace the word by any made up string of letters, and the definition would have the same effect: an indication of what you will mean when you later use that word. "That's a definition of what it means to say 'I flamjink X'." does exactly the same work as "That's a definition of what it means to say 'I believe X'." Uttering the latter sentence tells nobody anything about what anyone else means when they use the word "believe". It merely informs them of a personal decision that you have taken about how you will henceforth use the word.

But that is not the intended function of "No, that's not a belief, that's a definition of what it means to say 'I believe X'". It's an attempt at expropriating the word, an attempt to decree not merely how other people must henceforth use the word, but to decree that that is what they always meant by it -- what the word itself "really means". If that's what it "really means", then that's what everyone previously using it must really have meant -- by definition!

Rephrasing your next paragraph:

A definition is not true or false, it is useful or not useful. Why is this definition useful? Because it allows us to distinguish between two classes of declarative statements; the ones that are actual flamjinks, and the ones that have the grammatical form of flamjinks but are empty of meaningful flamjink-content.

Doesn't sound so convincing. It may very well be helpful to distinguish beliefs that are testable from beliefs that are not, and to make up a name for the former class (although "testable" seems to serve well enough already). But none of that deprives the non-testable beliefs of meaningful belief-content.

I would like to expand civilization as far as possible. If I attempt to send life beyond the cosmological event horizon, there is no experiment that can verify whether or not it succeeds. It would be useful to have some way of expressing whether or not I think sending settlers beyond it is worth the risk. I would call this belief that they'd succeed.

So I agree with what Protagoras said about the causes of the fall of LP: there wasn't really anything like a firm refutation, though important versions of LP like Carnap's were beleaguered by criticisms like Quine's attack on the analytic/synthetic distinction "Two Dogmas of Empiricism". I think the reason why LP fell was just that it went about saying all sorts of questions were meaningless questions, questions about ethics, metaphysics, etc. And people just got sick of that. The questions persisted, and our desire to ask them and talk about them didn't die out for the claim that all our attempts to do so were mere poetry. The nails in the coffin were really just a series of influential and brilliant philosophers in the 70's, like John Rawls and David Lewis who simply ignored the LP view about meaningfulness, and wrote books about ethics and metaphysics that people were interested enough in to discuss, argue with, or build off of.

If I'm right, this bodes ill for a revival: whether or not LPists are right about meaningfulness, people just find the LPist's world too impoverished to live in.

I suspect the claim "All beliefs are experimentally testable" is either vacuous or false. Our evidence for most of mathematics is deductive, not empirical. But it would be very strange to say that I don't have beliefs with substantive content about, say, the the Fundamental Theorem of Algebra.

You might say that mathematical investigation is a kind of experiment -- but in that case one wonders what causes for a belief aren't experiment. Is any evidence whatsoever 'experiment'?

The logical positivists said "All truths are experimentally testable"

Wasn't it more like "A statement is defined as meaningful if it's verifiable, and true if it's verified"?

Turn it on its head by asking what (truth / belief / claim) may not be (tested / questioned / challenged). If the answer is none, including this question itself, then you've got your answer. If you can identify something that is not subject to inquiry, that is known true and known in every detail with no further knowledge possible, I'd like to see it.