The London proof house (or Birmingham) will not play games with these conversion guns. While they don't care what the bore diameter is, they proof it using a 9.3x74R proof load. They will not and do not take 9.3 cartridges and special order .366" bullets.
So regardless of the bore diameter, whether it was lapped bigger or not, the proof house is shoving a 9.3mm cartridge in the gun and firing it.
400/360 was unobtainable in the 1960s-1990s and many were converted to 9.3x74r as a consequence.