Everything I've seen on the 6BRA since it became popular around 2017 has suggested that the 6BRA should be chambered 0.004" short of a 6BR go gauge, like any traditional Ackley cartridge, so that it is a crush fit on virgin brass. I don't know what the OG benchrest guys like Sam Hall and other BR shooters did 10 years ago when they were experimenting so I can't say what the "original" design is. I can say that when Alex Wheeler and Tom Mousel and others were popularizing the cartridge in the BR world in 2017 and it started setting world records, the recommendation was 0.004 crush on a BR go gauge. That would mean that the 6BR go gauge should be used as the NO go gauge for 6BRA.
All my 6BRA Barrels have matched this spec, including one of my Stuteville barrels.
From your description it sounds like your Stuteville barrel is perfect. Don't know if your Manson gauge matches the BR -0.004 spec or not.