et si tu arrêtais de voir le verre qu’à moitié vide?

ou bien

et si tu arrêtais de voir que le verre est à moitié vide?

que is used here to give emphasize to part of the sentence. So, which part do you want to give force ?

I suggest you to use the second: you insist on how he perceive how things are.

… Et si tu arrêtais de ne voir le verre qu‘à moitié vide ?

As you said, the “ne…que” is restrictive, and the place where you put it determines which object you restrict.

Et si tu arrêtais de ne voir que le verre à moitié vide ?

In this case you only see the half-empty glass, meaning you could also try seeing another glass (a half-full one, I guess), or at anything else really.

Et si tu arrêtais de ne voir le verre qu‘à moitié vide ?

Here you see only one glass, being half-empty, and you could try to see it differently (Half-full. Completely full. Completely empty. Who knows?)

While both options are grammatically correct, and are going to be interpreted the exact same way, I would use the second one as I believe the expression refers to a unique metaphorical glass being able to be half-full, half-empty, or as an engineer would say: unnecessarily big.