I think the glue method could lead to more serious damage as could the drilling option.
This is how I extracting the remaining jack stuck in the socket. I got hold of an unused indoor Ariel the telescopic type there's usually 4 or 5 sections each being a different diameter cut off the one that will fit perfectly into the jack socket push into socket turning the piece of ariel slightly, when it feels like it will go no further pull out the broken piece of jack should be attached to the ariel. It worked for me and took just 20 seconds. good luck.