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As you said, the serial number has a V in front of it. So it is V334xxx. The V series was made starting in April 1942 and continued until December 1944 when the internal safety was added and the serial suffix changed to VS (or in rare cases, SV). The V serial numbers began at V1 and went to V769,000. Therefore, your serial number is approximately 43% through the production cycle, assuming steady output, and that's a BIG assumption. That's a 32 month run, and 43% of that would be about 13 months in, so we can arbitrarily set an APPROXIMATE date of March 1943. That's as close as we're going to get and again I stress it is far from precise.
The U S Property GHD is a common stamping. U S Property was stamped on almost all of these guns from serial number V300000 on. (One source states this stamping, known to start around V30000, began in May 1943. This shows that the date above I calculated for March 1943 could be off by a few months. Your date likely is late summer or even autumn 1943.)
Even British contract guns had the U S Property marking, and of the 541,629 .38 S&W guns made for Commonwealth countries, 384,100 were supplied by the US Army Ordnance program and thus have U S Property on them. The terms were these were a lease, and when the British and others were gone with them, they were to be returned to the USA.
The GHD stood for Guy H. Drewry, who was the Ordnance officer accepting these guns. The GHD stamp took over from a WB stamp (another officer) in 1942 at s/n 145000. However, the GHD stamp was originally on the butt, but was moved to the top strap in May 1943 at approx s/n V300000. Another sign your gun was probably made in late summer or autumn 1943.
The BNP stands for British Nitro Proof for the 38 S&W. The 3 1/2 Tons per Square inch marking is what the gun is proofed to. I do not recall what the 767 is, but it is part of the proof testing. I vagely recall it might be an inspector number of the person doing the proof testing, but I don't remember.
The 5" barrel is standard for British contract guns as well as those supplied via the US Army to Britain and Commonwealth countries, but, 4" and 6" barrels were made too. These were all chambered for .38 S&W, also know as the .38/200 British Service Cartridge. The .38 S&W Special did not start production until Feb 1941, and they were only made in 2" (rare) and 4" barrel lengths. Most did not have U S Property markings, though some were marked U S Navy.
The finish should be a satin brush blue, not a shiny blue. Few doing a reblue would bother to put a satin refinish on it. They're either polish it, or bead blast it. If it is a reblue, the collector value is ruined. It only has shooter value.
Can you provide photos of the notches and the crossed out twin S's? I have no reference for them.
At one time Gun Parts and others had lanyard parts. Whether they still do, I don't know.