The adjustment screw on the TC triggers does not adjust the position of the trigger blades that trip the sear. The screw adjusts the movement of the front trigger before the rear trigger releases. It has nothing to do with the lock going into, or not going into the half cock notch.
Although the CVA and maybe some of the Traditions rifles locks have an adjustment screw for the sear, it only changes the amount of engagement the nose of the sear has with the full cock notch. It does not have a thing to do with the half cock notch.
If the TC lock fails to go into the half cock position there is a good chance that the nose of the sear has been damaged although it also could be as simple as loosening the screw that goes thru the sear arm to hold it in position.
A lot of people think all screws need to be tight so, they tighten them all up. Unfortunately, this is not the thing to do with the screw that holds the sear arm in place in the lock. This screw should be "snug" but not tight.
To see if this screw is too tight, remove the lock. Then, with the lock in the "fired" position, move the sear arm lever upwards. It should move freely and return to the former position because of the spring pressure that is on it.
Speaking of the spring pressure on the sear arm, it is also possible the spring was "adjusted" by the previous owner. If he compressed that coil spring to make it "lighter", he might have overdone it. If he caused the spring to be too short, it might not have enough strength to push the sear into the half cock notch.