Since I've been on a hinge replacement field-day lately - screw extraction is definitely something I can give some insight on.
You should definitely look at extracting it first to save the hassle of drilling and re-tapping. I've been using the premium Mastercraft screw extraction set. Basically, it has one end that you will drill a clean hole into the shank of the bolt. Flip and use the other end that threads into the hole. Once it has tapped itself into the hole, it will start applying pressure to turn. I've had best results using a socket and ratchet to do this.
It'd also help to apply a penetrating oil (PB Blaster recommended). My experience is that it kicks WD-40 and sticks around, acting like an anti-seize.
Hope this helps. We can chat at the Show and Shine if you are around.