Juan,
It was lucky that the standard centerdrill matched the plug taper and the minimum thread diameter. That is what surprised me. If you have the plug seated hard against the tapered seat, you can't do better than that!
Your pictures showed a 3-jaw chuck on your lathe. To use that, I would grab the front of the case and cut in thru the back. Do you have a test indicator? If you do, you can fit a drill blank into the existing crank hole and let it extend out and run your indicator against that. Then bump the case in the chuck until it runs true. The only hard part there is finding a snug fit pin. Of course, with this approach, you are going to have to run a bush the full length. I don't consider that a disadvantage at all. And you can prep the aft end of the bush with the thrust bearing face and oil grooves.
If you have a 4-jaw chuck, then you could grab the back of the case and go in thru the front. With a 4-jaw, you would definitely need to indicate on the case, but you can do it without the close fit pin by just touching the OD of the front end, and follow up by touching the bore to make sure they are concentric. With this method, you could just bore for a
Do you have a small (actually, tiny) boring bar? A holder? You can make one pretty easy if you wanted to. I would start with an 1/8 HSS drill blank and grind the tip to shape. I have actually used piano wire for a temporary cutter in a pinch. With the boring bar, you are not limited to what the reamer will do. You can adjust your bushing press fit into the case, in other words.
I suppose most guys (and most shops, too) work with the tooling that they have. It will define your possible methods. Not always the best method, but one that is possible. Instead of just dreaming about getting it done. Like me.