I haven’t looked at the specs on the BJAI, but we’ve got a few here running 6x55’s made by running a 6BR reamer in an additional .580 or so. 30° shoulders and minimal body taper (.460 at case/shoulder) on 6.5x55 Lapua brass. You might compare your print to the 6.5BR, you may find that it’ll work for sizing and eliminate the need for custom dies if that cartridge is what I think it is.