Removing snapped of headphone plug - tiny needle-nose pliers?

I have fixed, replaced screens, etc on several phones, tablets, etc. A friend of mine came to me with a good one. Her daughter managed to snap the headphone plug off down in the headphone jack of an ipad mini.

I searched online and found a method by which you pull the ink tube out of a bic pen, put some superglue in the end, and jam it into the headphone jack, let it fuse to the broken plug, and then pull it out. Unfortunately, this didn't work for me.

When looking down into the jack, there are a small amount of exposed wire out the center of the jack. If I could just find a tiny enough set of needle nose pliers, I could grab it and pull it out. I tried using some super sharp/fine tip tweezers but they don't have the grip strength. Any thoughts?