I see you are still struggling with this.
It sucks when you can be so close and get into the last nit picky things.
You are a few months behind me. I went the same route you have.
Helpful diagrams will not help you.
I have a few petcocks that are broken in different ways. The two spares I have don't have the same problem that your has.
When I get a minute, I will send you what I have. Perhaps you can make one working version out of them. This often becomes the only solution whit stuff this old.
The reason the petcock base turns is to allow you to position the switch in a place you can get at it when it's full tight. The one you describe that you have seems to have more than this as a problem though. I think you also told me in leaked from the switch. This part is riveted closed and can't be fixed.
I'll send you what I got but I'de say that you see if you can get your money back for the bad one and bid on the one I sent you as a link from my AOL "shenansdad" account.
Good luck. You seem to be in the home stretch. hang in there.