O-1 very short drift tip arbor punch tool made,  to get the pin started down and out of the slide, then you can use a standard punch to finish the driving the pin out one is start to move.

Short of this if the extractor pin fused to the slide channel when pressed in , and it will need to be drilled out via a mill (slightly undersized so you don't enlarge the pin channel) and replaced with a new pin.

And yes, get the extractor out before the you coat the slide.  With the extractor still in the slide, going to end up with a end of coating right at the ends of the extractor channel sides, and the first place that the coating it going to chip off the slide.

As stated, mill to under size drill the pin the channel drill entire way through the pin, which will the pin to be punched out on the easier side since the center channel in the pin allows the pin OD metal to flow inward on itself as it being driving out.

If you are trying to drill by hand, too much of a chance of veering off to the side, to enlarge the slide pin channel instead.

Hell, half the time your mill center drilling the pin, the heat alone and by the time you get to the the lower side of the channel drilling the center hole, the pin on the drill bit just ends up being pushed through the bottom of the slide by itself.

So slide Vised up square in the mill vise, start with center drill bit to indent the center of the pin, then as stated, much smaller drill bit that the pin to center channel the pin all the way through to start with/ so you don't end up drilling through the side of the pin to enlarge the slides pins channel.   If the pin did not come out with the drill bit, then use a punch to see if you can now punch the pin out with it center drilled channel.   If the pin is still fused to the channel side wall, then you can try a slightly larger drill bit, while even that drill bit is still smaller than the actual pin OD.