Where I worked we held close tolerances and sold parts that met them. We had plaques from RCA and Kodak for going a year at a time with zero rejects. We weren't trying to hold any better than we could make but we did precision work within tolerances every day.
Part of it is not trying to hold impossible tolerances, but you have to know not only what's possible but what's practical in order to do business. Not just theory, we made the parts.
Why not turn the windings at 1 diameter + (tolerance * 110%) apart per turn? When you come back across the new layer will sit on top. Or is there some reason why the windings have to jam in side to side all along the coil? Does this wire vary thickness by even 10%? You'd get a tighter pack if the diameters set in a hex pattern anyway.