I had a similar horror story trying to drill through the front lug on a iron mounted English fowler trigger guard. Having only drilled brass lugs I thought I could easily pop a hole through the lug, first drill bit, "POW" it broke way down in the hole, second drill bit from the other side "POW" way down in the hole.
The trigger guard was now pinned with broken drill bits and wasn't coming out. I had yet to shape the stock and worse I had put a temporary phillips head screw to hold the back part in place, It was under the bow and I couldn't get to it to remove it.
I finished shaping the entire underside of the gun around the trigger guard and wrist with a small riffler file and sandpaper, it took forever.
A few days later a guy on here said to go buy a 1/16" carbide tipped bit, put it in the hole and let it eat with only the weight of the drill motor pushing it down.
I was sceptical, but did as he said. After a full 15 minutes of running the drill I saw a metal chip come out of the hole, a couple minutes more and the bit went through the lug and I could remove the trigger guard.
I found the trigger guard steel was so hard that I struggled to drill it with a new bit in my drill press. I soldered on a new mild steel lug and completed the job.