If it's that intent on staying, leave it in peace. When you go to insert the part, just hit it with the soldering iron again.
And the will therein lieth, which dieth not. Who knoweth the mysteries of the will, with its vigor? For God is but a great will pervading all things by nature of its intentness. Solder doth not yield himself to the angels, nor unto death utterly, save only through the weakness of his feeble will.
If you're more intent on getting it out than it is in staying put, quickly but very gently inserting and removing a heated drill bit should make short work of it. Push it through at least 1/2" on the other side to let the solder end up in the grooves. Better: push it all the way so the grooves of the bit go completely out the other side. If you weren't slick enough, you might need to grab the last bit with wick or a bulb, but don't do this if you still see solder on both sides or deep inside--just use the bit again. Or you could just push it all the way through--a one way journey through the through hole--but don't ask me how to hold such a hot bit that way. You could drop it, but dropping a hot drill bit full of molten lead is a dumb thing to do (tm). I used to put it in a flat wooden clothes pin and heat the tip of the bit with a lighter or... maybe a candle... I really don't remember. Wood's good because it won't suck up the heat, and is more resistant to flame than plastic. Try to choose a good quality wood, like hickory. It'll fill the room with that nice pleasant smell of burnished wood, give you a sense of accomplishment, and that sense that you're in a real work shop, and is therapeutic besides. The bit should be hot enough to melt the solder on its own. Just use the bit, not the iron, and you'll be sure. Just don't apply any pressure--the bit should almost fall through from its own weight--it really won't but you should only use the slightest pressure only to overcome the drag from the molten solder. If the solder's will is truly fantastic, and you need to try again, just push it though (gently) as far as your makeshift handle lets you and leave it to cool off. If it gets stuck even a tad after cooling off, don't pull twist spindle or mutilate not even a hair's breath, just reheat the bit near the hole. You might want to constantly twist the bit slowly while it cools to prevent it from sticking, which is why you want to get it in far enough so it's past the groove part of the bit. While not crucial, try to use a bit slightly smaller than the one used to drill the hole. You want a smidgen of wiggle room or you'll risk pulling the pad off. I have no idea what kind of bit I had, but the solder never stuck to the bit. Well, not bad enough that a metal tool couldn't get it off. All I remember is the bit was silver colored, so it was probably stainless steel, as amb mentioned earlier.
They should make a soldering iron tip shaped like that.
I still think doing nothing is the best option.
