One more thing, and this really helps to solve whatever problem may have existed.
I'd first realized that the quill was smaller and the steerer tube narrower when I tried to stick a 10-year-old welded aluminum quill stem into the Schwinn Traveler, instead of the old forged SR stem. The newer stem didn't fit into the head tube. In fact, the wedge (which was made of aluminum on that newer stem) didn't even fit through the headset's locknut.
However, I've got a Nitto quill stem, for standard 22.2mm steerer tube, that had a steel wedge on the bottom. On a whim, I tried to put the steel wedge into the steerer tube of the Schwinn, and lo and behold, it fit! And this despite the wedge having 0.875 stamped on the bottom (0.875" = 22.2mm). So, I replaced the off-kilter-drilled wedge with the wedge from the Nitto stem, and will grab another newer designed-for-22.2mm aluminum wedge to use with the Nitto stem whenever I start running it again.