Honda EK's are made very strong in that area, if you're talking about the shock tower when you say turret. Your car isn't heavily rusty right? That's the only time I've seen a shock come through the tower, and it was not on a Honda.
First you should eliminate any variables with the car's weight and suspension.
-Remove stuff from the car if you carry anything significant.
-Even out your tire pressure all around.
-Set all your bushings correctly, because a bushing that is binding will affect the suspension tightness. This is done by putting the car up on four jack stands with the rear tires still on. In the front corners, put the jack under the LCA and raise it until that corner comes off the jackstand (putting that corner at ride height). Now loosen and re-torque each bushing to spec, the fork to LCA being most important but you might as well do all underbody bushings to be sure that they are not under load with the car at ride height.
For the rear you can put the E-Brake really tight and put the jack+wood under the wheel or use the rear LCA. Do the same procedure with the rear bushings as you did with the front. Since it's best to torque them to spec with a torque wrench, find a Haynes or Helms manual if you don't have one.
-If you have adjustable endlinks, while the car is up on stands, preload both wheels (front or rear) so that end is at ride height. Adjust the swaybar endlinks so there is no twisting in the swaybar.
You may want to have a friend see if the heights change with you in the drivers seat, or vice versa.
Another option is to swap the shock+springs left to right. Not too bad of a job and it might make a difference. If it worked and made you happy then you would be good to go. If it did work, and nothing else you've done has had an effect, then your shocks and springs especially aren't in even condition, either from wear or manufacturing defects.
But, keep in mind that these car's do not weigh the same at each corner. To make the weights more even (and totally nullify your current problem) you would have to buy adjustable coilovers and corner weigh the car, which involves changing all ride heights to slightly different heights to even cross weight percentages.