Well, cold contracts air and expands water, so to me it would shrink up the air cell and expand the white, which could further detach it. In addition, the refrigerator has a drying effect, which may also be detrimental.
Using only the worst eggs really isn't a good way to test the hypothesis anyway, because if it doesn't work you won't know if its because of the refrigeration messing up, the air cells being too bad for the refrigeration to help (if it were possible), or if the refrigeration had no effect but the air cells were just too bad either way. You would only be testing whether refrigeration helps really bad air cells, and your sample size is too small to make a significant conclusion.
Re the gyroscopic shipping container... would you want to pay for that? Granted, its a total waste of money to order eggs and have them arrive scrambled, but people do have good success with them when they are packaged properly. The problem is not knowing if the seller did package them properly until they arrive.
I suppose if you want, you could take a few fresh eggs and mark the air cells. Put them in the refrigerator and mark the air cell every day or so for a few days or a week. Give some more a good jostling and detach the air cells, and do the same for comparison. Have two control groups (detached and intact) that sit out on the counter that you also measure.