I have several older L lenses and one has always driven me nuts. It just never seemed as sharp as it should be. The lens in question is a 24-70/2.8 L ver. 1. I really want to like it, on my 20D I could make super sharp images but they were not very common and on my 7D I just do not get the number of sharp images that I expect. I do find that I use it at 2.8 often, but with the L lens I should be able to whenever I want to.
My 17-35/2.8 and 80-200/2.8 are almost always sharp the latter is amazingly sharp, sometimes I have to take some of the sharpness out in PP so as not to offend the subject. I also have a 300/4 IS that is just tack sharp. Point being, I think my methodology in taking the photos is fine.
I am in east central IL, where would a lens have to go for calibration and would they need all of my cameras to average it or is it set to some spec and returned? I have never considered going through this process before, but I really want to up the positive output from this lens. I do get to Roberts from time to time, love to drool on the gear and like to support brick and mortars. They also clean sensors while you wait, for a reasonable fee. I have never been comfortable with that process.
Before you send your lens off to Canon or incur any expenses, I would recommend trying to perform an AFMA (Auto Focus Micro Adjustment). It is possible to do on your 7D. A free and accurate method is Dot-Tune, which was developed by FM member snapsy. The video tutorial is helpful, and if you have any issues, that thread is still active so you can post to it and usually get a reply from Adam.
So, start with AFMA and see what that gets you. Also might help to post a few samples with EXIF intact so that people can help troubleshoot. If AFMA doesn't solve the issue, Canon can check your lens and camera for any needed adjustments. However, it most likely would not be a free service.