I am a tech facilitator at a high school. We just started a 1 to 1 initiative, providing an iPad for each student to use. Within a few days we had our first charger broken off in the iPad. The first solution I found online was the super glue, using the other part of the charger. I got a pretty good bond, but it broke apart when I tried to pull it out. I may have gotten a little glue in there, making other attempts harder. However, the chargers snap in there pretty good anyway, so I'm not sure that it was anything other than the normal required force to pull the plug out that caused the bond to break
I tried the seam ripper. It started to move the charger end, but then seam ripper broke. It might have worked if it had been better quality.
Finally got it with a very small screw driver. I had to be pretty rough with it, though.
It works fine. However, the charger plug (a new one, of course), does wobble a bit more from sided to side than it does in a different iPad.
Based on this experience, I am inclined to think that super glue using the twist tie ends (or something else -- maybe an appropriately sized cut off zip tie) might be best to try first. Putting a drop of super glue on paper and dipping the chosen tool in it to get a controlled size drop sounds like a good idea. You want enough glue to completely cover the end and fill all space between the 2 surfaces to be joined, but not much more, to minimize risk of glue going where you don't want it to. If you use something smaller than the channel, but still big enough to get some surface area, and if you use good technique, then I think there would not be much risk of gluing it in there worse. Overall I think this is a "gentler" method than the seam ripper or tiny screw driver method, which in my case resulted in the new charger plug not fitting quite as snugly as before.
I agree that the design seems flawed. Another tech facilitator in our corporation (based on the appearance of the plugs) predicted that we would have problems with this. Beyond that, apparently some are defective.
With a total of nearly 2000 of these in the hands of students (grades k through 12) in our school corporation, I expect that I will have another chance to try it sooner or later.