You thought wrongly then. You integrated from -L/2/(1-v/c) to +L/2/(1-v/c) which is the width of the retarded distribution. The unretarded distribution extends only from -L/2 to +L/2. Of course, your integration limits are correct (provided the propagation speed for the static electric field has indeed a finite value c), but you failed to take into account the correspondingly reduced charge density over this interval. Anyway, I believe I have heard enough now in this matter, and I think I'll be able to progress from here and develop this further on my own. I thank you for your contributions which have helped to clarify the issue for me.