I’m concerned about this talk about tightening the screws more. If the jaws are set up right, it shouldn’t take more than a half-turn past contact at the bottom screw. That should produce enough clamping force to hold almost any blade. If not, then something else is going on. Excess torque on the bottom screw can bend the vise jaws.
Your symptoms point at a jaw which is only making contact at the bottom of the blade. To repeat what others have said here, the top screw is only used to set the position of the jaw relative to the knife. The lower screw is used to tighten the vise. A half-turn on the lower screw will produce hundreds of pounds of clamping force.
I second the motion of using painter’s tape, but pay close attention to the alignment of the jaw at the face of the knife. If anything, you should leave the top screw slightly loose, so that when you tighten the bottom screw, the vise closes at the top of the jaw first. Ideally, the jaw faces should fit flat against the blade faces. The diagram below shows an exaggerated view of how the jaws should be positioned relative to the blade.
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