Gostrider,
The proof date of 8/24 indeed, indicates between the wars production rather than pre or wartime production. It never hurts to do a chamber cast, but you can check it another way. The 7.7/57 is not actually the caliber nominal designation. The 7.7 represents the proof house's actual measurement of the bore (not groove or bullet) diameter. The 57 represents the maximum length case that will fit into the chamber, regardless of shape or other dimensions. There are at least 3 nominal cartridges that would fit the proof mark 7.7/57, at certain times. The most common is the 8x57IR (aka 8x57JR), there was also 8x57R/360 and the little known 8.25x57R Hagen (aka 8x57 Express), both of which were based on the British 360-2 1/4" case. Since the 8x57IR was based on the 8x57I m88 case a 30-06/308/270 case, upside down, will fit into the chamber, but will not fit into the other two. An upside down 30-30 rim will almost fit their rim recess however, providing another means of distinguishing between them and the 8x57IR. A "J" (or "I') would not be part of the proof mark due to being part of the cartridge's nominal designation rather than a measurement of the barrel/chamber. A "R" is not marked because whether it is chambered for a rimmed or rimless cartridge is obvious by observation of the chamber mouth.
Mike