Carefully inspect the OD of the tapered part for nicks. If you find any, file them off. Then sand it smooth with some 320-400 sandpaper. Don't go crazy with the sandpaper, only spend a couple of minutes.
Next, you need to clean out the bore of the spindle.
When you insert it, you need to align the tab. Once you have it aligned ram it in quickly. Then unwind the chuck until the three jaws are fully recessed inside the chuck. Now give it a couple of taps with your brass hammer.