Yeah, all that chromium just loves to form carbides. It's so common for the hole to work harden though. From your description of drill bit performance that's what I'd think too. Stick with the simplest solution.

Holding with a magnet will work, until the steel becomes non magnetic, and it should have took off across the room when it let go. That'd be hot enough to quench to hard. Doesn't sound like that happened though.

It looks like you got a great weld, pretty stuff for sure.