I don't have a Mk III to check, but I doubt very much that pin is in a blind hole; Ruger doesn't do things that way. Have you removed the barrel and receiver from the grip frame and checked it out?
Oh yeah. The barrel is bare. "Blind hole" is the term, and I think this classifies. Item 7 is the pin I want out. Items 4 are just fillers, which are for, and now hold, a Weaver rail. And no, the other end of the pin is not visible from inside the chamber. It is pinned in solid stainless.
Anyway, don't go drilling until some of the other folks are heard from.
I'm there. I'm in no rush. Haste makes waste. Learned that the hard way.