There may be a way to locally anneal the area. Many years ago I had a similar problem and had read somewhere that using the head of a nail to anneal a small area can work. I clamped the blade I was drilling to the drill press table and brought the head of a 16-penny nail into contact with the metal. I ran the drill press at high speed and used a fair amount of pressure and the area under the nail head got red hot. I let it cool naturally and drilled through without a problem. It didn't seem to affect the hardness of the rest of the blade. Now, this was over 20 years ago and I'm going from memory so the details are getting dimmer but the general process is right. If you try it, maybe do it on an old spare blade first?
Oops, you just posted the photo above - too late!