If the 1905 were mine, I`d leave it as is, other than repairing the rear sight etc.. Looking closer at it, there are some of 1905-R features, and the front sight would also be correct for a 1905-R.
I did not make out the Circle P until you mentioned it. This is normal stamp on a 1905-R, but that one looks like it might be humped.
Are there any numbers under the buttplate? It is also worth checking under the buttplate on the R-10 (numbers are usually quite small, last two serial numbers, stamped in the steel)
I also wonder about the lack of serial numbers on Ross factory sporters with all the other factory markings.
I do know there are others out there. I have seen two M-10 .280s, Two Civilian MkII**s and at least five 1905-Rs.
One of the M-10s was featured in an article in Man at Arms magazine if anyone cares to look.