Chuck the barrel up muzzle to the headstock - better yet use centers .
Mount an indicator to the compound and adjust until the indicator stays
steady when you crank it in and out .

Almost there, but the barrel is in the action. Ooh, here's the
thought... cylindrical action, not perfect, but chuck it up, run the
muzzle very carefully onto a tailstock live center. Use indicator as
described. Snap, that's backwards. Unless I indicate the far side of the
barrel...