What do you think of this solution?
I found that just gluing the broken piece didn't exert enough downward pressure on the cable. I tried 4 different glues: Loctite SuperGlue Gel being the best because it was thick and didn't run down into the connector and it sets within 30 seconds (because I couldn't find a good way to safely clamp it while the other glues set in 20-60 minutes).
However, in the end, a wooden toothpick worked perfectly and I didn't use any glue at all. The duck tape doesn't do anything, I just didn't want to remove it after finding something that works.