Huh? We're talking past each other here. ... I'm talking about logical possibility, not existence.

Oh, oops. My mental model was this: Consider an all-perceiving entity (APE) such that, for all actually existing X, APE magically perceives X. That's all of the APE's properties -- I'm not talking about classical theism or the God of any particular religion -- so it doesn't look to me like there are logical problems.

If there's an all-seeing deity, P is well-formed, meaningful, and false. Every object is perceived by the deity, including the deity itself. If there's no all-seeing deity, the deity pops into hypothetical existence outside the real world, and evaluates P for possible perceiving anythings inside the real world; P is meaningful and likely true.

Mostly agreed. But that's not the GEV verificationism I suggested. The above paragraph takes the form "Evaluate P given APE" and "Evaluate P given no-APE". My suggestion is the reverse; it takes the form "Evaluate APE's perceptions given P" and "Evaluate APE's perceptions given not-P". If the great APE counts as a real thing, what would its set of perceptions be given that there exists an object unperceived by anything? That's simply to build a contradiction: APE sees everything, and there's something APE doesn't see. But if the all-perceiving entity is assumed not to be a real thing, the problem goes away.