It worked!
I started the original hole just a teeny bit off-center, so I drilled it sideways just a little to center it and then counter sunk the lead-in a little bit and finished it with a 27/64 drill. The tap led right into the original threads. I was lucky. It picked out the remainder of the steel and I extracted a perfect ring from the end of the tap. The plug sits in a little deeper now, but at least I do not have to go oversize.
I would have considered threading in a larger blank and using Loctite, or perhaps braze/silver solder to hold it in. Then drill and tap a new hole the original size to restore the case rather than going oversize.
MERRY CHRISTMAS EVERYONE