Nice rifle. I have an arsenal rebuild 03A3 with a BA-W.L. stamp exactly like yours. Mine also has an OG stamp, so I can't be sure where the rebuild was done. Mine has a pristine replacement barrel dated 12-43 (nine months later than the receiver mfg date). Does yours also have the OG stamp? I have not been able to learn anything specific about Benicia's postwar work; it was a feeder for San Francisco Port of Embarkation on the outward bound side of the war effort. I have only seen a handful of 03/03A3 stocks with the Benicia stamp (plus a couple of carbine stocks). With two rebuild stamps I can be even less certain than you when the stock came to be mated with the barrelled receiver.

My best wild guess is that Benicia may have done preliminary receipt, sorting, inspection, and cleaning of rifles returning from the Pacific or used in west coast training camps and passed them on to better equipped facilities for rebuild. Again, this is just a guess based on the fact that Benicia was a larrge operation during the war yet only a few stocks seen today are so marked.