Not a definitive answer, but-----we can tell this from the information you provided:
---A proof P was stamped after manufacture, & every time there was a US arsenal rebuild; so, it was rebuilt at least twice.
---RIA/EB = Rock Island Arsenal/Elmer Bjerke
---4 digits of the SN would only have been scribed/stamped by a FOREIGN military armory, never a US arsenal.
---All Greek lendlease return rifles sold by CMPabout 10-15 years ago were packed in grease.
---Chamber adaptors were readily available commercially for many years; a gunsmith can readily confirm that's what you have with a borescope, & he can also easily remove it with broken case extractor if it is stuck.
---Peep sight is the most obvious change in the 1903A3 from the 1903.