Mini mill gibs are not tapered so that's not the issue.
For clarity, when you say "tight in one direction only", do you mean something like "it's tight when I move the table to the left but not to the right" (or substitute "forward" and "back"), or "the Y axis is tight but the X axis is loose"?
Since you refer to a single table screw I'm guessing the problem is specific to a particular axis but I could be wrong. Even if my guess is correct, there are significant differences regarding the X and Y axis. The X axis has thrust bearings in the bracket, so the nut on the handwheel can be tightened down pretty good without making it difficult to move the table, but the Y axis uses thrust washers, which require a lighter touch to prevent the feed screw from binding up. It would be nice if both axes had thrust bearings but for some reason that's not the case.
So we need to know which axis you are referring to.