do lots of this type of work, I will usually make a sleeve already threaded in this case 1/2 28, the center is reamed as 3/8, next turn the barrel under the sleeve diameter 0.002 to 0.003 and heat the sleeve, slip it on and done, it will align perfectly and avoids setting up the barrel twice
I agree that this method works very well for most industrial applications, however I don't mind setting up twice to insure it is as perfect as modern equipment can make it. With your method I can envision several potential problems for minor misalignment. I was taught that when over sleeving anything that one should start with an oversize OD sleeve and final machine to spec after sleeve has set and cooled.........may or may not be better, just makes sense to me.