I would leave it alone but im picky and something like this will slowly drive me insane.
Because the screw is tight, all other methods have not worked and you've got all the time in the world.
I would get a needle or some other hardened picking device and start poking around the outer edges of the ball driver.
If you can locate any dental picks, that would be even better.
I would attempt (through manipulation and picking) to provide clearance all the way around the head before attempting to remove it again.
Many times, if a person is very patient and meticulous, they can get the broken piece to move slightly.
Caution here should be noted though; you do not want use so much force (when picking) that you break a piece of the pick in there too.
That would be hurtful, not helpful.
If you get it to wiggle in place, you are one step away from getting it out all the way.
I would use the heaviest needle you can find that will still allow you to fit it in any open spaces available between the head and the screw.
Maybe even two needles eventually so you can lever one off the other, once the head has loosened up some.
I'm talking jewelers loop, very fine picking kind of manipulation.
I would not suggest something so meticulous to anyone unless it had worked for me in the past.
I would not add oil or any other lubricants into this picking type of scenario, too sticky, you want it dry.
There must be a burr of some kind holding this in place.
You will basically be clearing all obstacles from around the hole (burrs and such) and then once the object is free and clear of the obstacles; use the two needles to lever the head out.
If the head is very loose but does not seem to want to lever out; then that's a sure sign that not all the obstructions have been taken care of.
Return to poking/picking until all obstructions have been cleared.
