I ended up making a new center punch for this setup and it works much better. It can be tapped in with a rubber mallet too, so there's really no danger of deforming it.
Because I'm heat treating with a general purpose propane torch (why haven't I gotten a MAP torch yet?), the HT on the part isn't super even. I don't think the part that gets pounded is particularly hard, but the business end is impervious to a file, so all is well. :D
Now I wanna make all the parts over again, but better. Having gotten it all to work, I have a much better idea what I'm doing.