My guys do the same thing. They meow obsessively because they know it will eventually get you to feed them. They do it because it WORKS. And if you ignore them, they get annoyed because meows worked in the past, so they ramp it up and become more obnoxious. They don't understand why something that worked in the past isn't working now. So they meow louder, longer.
I've been working on ignoring them. They've been working on how to become louder and more obnoxious. Pouncer discovered how to bite the handle on the lid of a decorative jar, pick it up, and let it clang back into place, drop, repeat. MUCH more effective than a simple annoying meow. The others simply start knocking stuff over. But we're still ignoring them and not feeding them. After a while, they give up. But its after a loooong, noisy, and headache inducing while.
We're winning. Evenutally, they will just stop it all together. Its a process that will take some time. we've been doing it about 2 months now. It would have gone faster if my husband would be 100% consistent, but when he's tired or frustrated he doesn't want to deal with the meows coming from 7 cats.