Both of those are pretty much how I would do it with a 4 jaw in a shop set up to do this. My advice is based on a low volume home job using a 3 jaw chuck. Remember also that this is not a new-blue sporting rifle. Finish is already 125+years old. Three jaw, lock headstock, tape bbl, towel over ways, and hacksaw to start. Unlock headstock and face to square. Very likely could crown to "19th century contour" with a file against the spinning work.
Now if he has a 4 jaw... Mandrel and dial indicator = perfection. You guys are dead on right.