DAMN that rough!  That's one of my "fears" when going after antique firearm screws and whatnot. It's hardened, but not tempered so it just "breaks" like that.

Limited experience but the original Krag screws I have seen are not that hard. I see many on this forum with buggered heads from cheap screw drivers, indicating they were not very hard.
Some of the replacement screws I made for mine were from W1 tool steel, then hardened and tempered till I got nice looking to a color blind person oxide colors. The shop made screws were many times harder than original. On my sporter build the trigger screws were run in and out MANY times with no damage to the slots.
Part of your problem maybe the high speed drills. A micron thin hard coating does not help in drilling hard material the underlying material will get deformed and the drill becomes instantly dull. Machine shop grade carbide cutting tools are needed for real hard stuff.
Looking at the end of the broken screw I did not see the fine grain structure that usually goes with a very hard screw. Try a known sharp file on it. If it skids across without cutting, it is really hard.

An example of removing a very hard screw. I dulled a couple of quality drills using a hand held drill motor on this broken off stud in a lathe bed. Only 3 studs are used and this one was so hard I thought it was a broken off form tap. The other studs were missing when I got this lathe so I did not even know what was broken off in there.
Since the first attempts failed I bolted the bed to the mill table and milled a flat area on the screw then drilled it with a carbide spade drill that I sharpened for left hand rotation. After a while the bit grabbed onto the stud and screwed it out. Carbide drills require a rigid set up or they will shatter like glass and the mill allowed a heavy accurate feed so it did not just rub on the surface and make it harder. These carbide spade drills are sold as "die drills" for tool and die makers to drill through hardened die sections.

Back to Carbon Outlaw, a close up picture of the threads would help diagnose if the screw is original. And a brush with a file will tell if it really is that hard.  Your diamond drills mention grit size so that would indicate diamond dust held on with a nickel plating like a diamond knife sharpening hone? If you drilled that with a hand drill you are a better man than me. For a original screw to be that hard would mean it was actually heat treated and missed the tempering operation. To me that would be a surprise as they ones I have seen are so soft I would not have guessed they had any treatment.