Use small mole grips (smaller teeth) done up tight. If your grips have a toothed section near the hinge:
And it will close tight enough there, use that instead for more force. Have the grips flat against the post, not sticking off the end of the screw like a screwdriver would.
Like this:
NOT like this:
If by grips you mean water pump pliers, use a decent brand, grip near the hinge and squeeze hard. Consider getting some mole grips (vice grips, self locking pliers)
If you have a grinder and a steady hand, you can grind a small flat top and bottom of the screw by removing the threads only, which will help. If trying the drill chuck method, grind a triangle of flats
Go steady; these screws have already demonstrated they will snap once, and quite likely it will happen again
If none of it works (they're self drilling screws, but you mentioned pilot hole, so perhaps your newel is hardwood; travesty that it's painted but helpful in this case) just use a flap wheel in a grinder to grind the screw peg all the way flush then sand and paint the area
Go steady; these screws have already demonstrated they will snap once, and quite likely it will happen again That they're self drilling may have worked against you given that they will have chewed the inside of the hole up and generated a lot of heat as they went in, effectively creating a heat setting glue that grips the rifling on them and the hole sides. If you were desperate to get it out, finding a way to heat them without damaging the wood would probably help, but I do think you should commit to just grinding flush and making good if they won't budge