When you tighten the screw very tight, is the headset binding making it difficult to turn the bars? Or is it just the screw that seems to be getting awfully tight?

If the latter, it's likely that the steerer is a bit long and the top cap is bottoming against the fork rather than pushing the stem and spacer stack down to compress the headset.

If the former, you headset might be missing the centering cone, so while you're compressing the bearings, but not securing the top bearing to the steerer.

BTW- I should have said this first, you are loosening the stem before trying to adjust the headset, aren't you?

First step is to confirm the steerer length. Tighten the stem, remove the top cap and check that the fork ends about 1/8" below the top of the stem and spacer stack. If so, the next step is to loosen the stem, and pull everything above the upper bearing off and confirm that the centering cone sticks above the headset slightly and the spacers can push it down to secure the headset.