Quote from local boy "A statistical sampling was made service-rifle barrels during production runs to ensure that they did not exceed maximum and minimum standards."    Fore runner of today's statistical process control? If so one with a star gauge mark would be no better or worse than the ones that proceeded or followed.

  Quote "Beginning in 1921, barrels so gauged had a tiny eight pointed star stamped on the crown at the six o'clock position.  Additionally, beginning in 1921, all barrels for competition were star-gauged and so marked on the crown." The ones that had additional inspections for competition or sniper use should have been marked differently than the ones just star gauged to have any meaning as to absolute quality.

When you have a stabile process in making things you check only one in so many parts to assure part tolerance. Deming taking statistical process control to Japanese auto makers, was just helping them understand things that were done by Ford on his first assembly line and apparently pioneered by SA. US automakers forgot some of the early lessons and suffered for it trying to push production and not shutting lines down when problems arose.

If Local Boy's quotes are accurate, star gauging with indicators started in 1905 (whoops not 1921), before that they probably used "star" shaped hardened go and no/go plug gauges. Both style gauges would need to be twisted to follow the grooves.
Paying a big premium for a marked barrel seems a waste to me.