There probably are legitimate rifles (target maybe?) with serial numbers "across the top of the barrel reinforce". Not to be a stickler, but neither of your rifles are numbered on the top of the reinforce.

Bluenoser`s rifle was most likely numbered on the left side originally. I am pretty sure of this because, I have owned quite a few 1905-Rs and have seen plenty more. I have rifles with both higher and lower serial numbers than his rifle.

They all have the serial number on the left side, except a couple that have no serial on the barrel (replaced).

See post #28, I have a 1905-R that has the proper serial number on the barrel in the normal location, this number matches the numbers on the stock. It also has a different number partially hidden by the stock, that goes across the chamber, much like your 1905-M, only on the other side. Obviously this is not a serial number on this rifle.