M1903 barrels are hard to come by, while M1903A3 barrels are still around. But since many 03A3 barrels look like they were turned with a dull hatchet, I recommend re-finishing them to match the original 03 barrel.

The 03A3 barrel has its witness mark visible, so I suggest turning it to the right size for the FRSB, then installing the barrel, then the 03 FRSB, then drill the cross pin hole.* If the barrel is new, it will be short chambered, and must be reamed to get the proper headspace.

*Watch that part; you need a very stiff starter drill to begin with.

Jim