No, you are not over thinking things at all. You need to get that screw in the proper location. In my mind, the top tang screw being a wood screw on the Flues is a design flaw.
To locate it properly, turn a bushing on the lathe that barely fits the hole on the tang on the OD and drill the ID to the minor diameter on your screw. By doing this in one setup on the lathe you will maintain concentricity. Make the bushing at least 2" long or so in order to have something to hold on to when drilling.
Best of luck,