Charlie, I hate to tell you, but what you're trying to do isn't easy. It can be done, but honestly you probably have neither the tools nor experience to do this "correctly". Not that that should stop you from trying.
A carbide drill in hard steel has a narrow processing window that you're going to find challenging. I don't think this is something I could do manually on my Bridgeport without tearing up a twist drill.
With that said, these are the things you need to focus on:
The primary problem will be over feeding, which will break down the cutter pretty quickly. The force required to get the drill to cut will be surprisingly high. The web of the drill has to penetrate your work piece (which is made of hardened steel) and a drill web is a pretty blunt cutting tool. The difference between the correct cutting force (fairly high) and too much cutting force (a little bit higher) is pretty narrow. You need to back your work piece with a piece of steel or you'll blow it once the web exits the back.
Chatter will dull a carbide drill. Run it as fast as you can without chatter. This is highly dependent on your mill. I'd run a carbide drill in A2 at 800 RPM but YMMV.
Unlike many of my diatribes about people needing to feed their drills harder, this is not the case here. Underfeeding a drill wears it by abrasion which isn't going to be a problem here (and hard A2 isn't exactly going to work harden much more than it already is). You just need to feed it hard enough that it doesn't chatter, yet not so hard that it breaks down. Good luck with that.
Coolant or oil is not your friend. Honestly, the hotter the A2 gets the better it will cut here. But someone blasting the tool with air will prevent you from recutting fines which would otherwise tear up your cutting edge.
A spade drill or a straight flute drill would be more forgiving.
Please report back with your results!