I'm not much of a video guy, but I tried to make a quick demonstration video, showing how I'd do it...
https://vimeo.com/158523117
I forgot to mark it with a Sharpie, but that's the basics. The blade never got hot... when I make repairs like this, I don't cool hot blades, I start with the blade cool, and as it warms up, I had a bucket of water I re-cool it in. (It didn't get as warm as the phone did making the video).
After the point where I turn the sharpener around, you can see there's still not quite a point, and a now a thick edge. So at this point, start grinding in a new edge, as that comes together, the point will form... then blend it all together when you sharpen it. (Oh yeah, you may want to dull or tape the whole edge first...)
Not that great a video, just wanted to show a demo. Yours will obviously take longer, but you don't have to do it all at once, work on it a bit and as I tried to show, check often! Hope that helps.