And further, since I do not want you throwing shoes -" Professor Quirrell made another gesture, and just within a globe intersecting the Greater Circle of Concealment, a slight shimmer appeared in the air. "Thiss barrier will explode if touched, by you or other material thing. The resonance might lash at me afterward, but you would also be dead.

So I guess Q disabled the Greater Circle of Concealment and the Globe before taking the Cloak.

I suppose it's all moving very fast, but shouldn't Harry have triggered the barrier to explode once he heard the story on how the Process of the Timeless worked? Quirrell's taking the cloak from him is predictable at that point.

Kill the hostage (himself), and at least momentarily incapacitate Quirrell before he can get the Cloak. Seems like a strong play.