Its tough to draw absolute conclusions from the stock markings. Like anything else in the military there are rules and then there are exceptions to them.
The SA within an open box stamp appears on Springfield Armory Garand overhauls/rebuilds done thru the 1950s into the early 1960s when the electro-pencilled marking was adopted. It was not US practice to add rifle s/ns to the stock.
I have 3 M1D stocks. One is on a Danish Surplus M1D. It has the SA open box stamp, the Springfield "P" firing proof and also has a Danish addition of the rifle s/n stamped on the top edge of the stock below the windage knob (Danish practice was to stamp the s/n on rifle stocks on the bottom of the butt on most, but not all, of their Garands). It doesn't have holes drilled on the bottom of the stock for check piece mounting screws which were normally installed at unit, rather than armory, level.
Another loose/spare M1D stock has no markings at all, but is drilled for the cheek piece screws. My assumption is that it was a replacement which was installed at base/unit level.
The 3rd M1D stock has the SA open box stamp, the firing proof stamp, the ordnance wheel stamp and another stamp which I can't ID. Its also drilled for the screws. I assume this one was originally installed on an M1D by Springfield Armory with the check piece installed later at unit level.
I'd enjoy the rifle for what it is. I have a spare M84 scope and mount, an M2 flash hider, a NOS M1D barrel, a M1D rear handguard and a cheek piece which I'm going to assemble on a Springfield Armory receiver at some point using one of the spare stocks mentioned. It will be indistinguishable from an armory assembled M1D and will be valued as the sum of the parts.
Reproductions of all unique M1D parts are in circulation so people need to be careful on these.