The slugging is a good idea and I think I'll do it since I have no idea how much it has been shot. (It's a 1937 manufacture) And 7.62 mm does convert to .308" which does work in my American made .30 cal. rifles.
I'm not sure, except for the '3 line' specification (.30 caliber) how the Russians arrived at bullets several thousandths larger than .30 cal.
The whole series of .30 cal rifles included the .303 British, the 7.7mm Arisaka and the 7.62 Mosin, all of which are larger by a few thousandths than .308.
Anything under a 7.92mm, usually referred to as 8mm, seems to be a .30 cal.There doesn't seem to be any .31 caliber cartridges.
It's a European convention of referring to land diameter rather than groove diameter.
The .303 British has a .312" or 7.92mm groove diameter but has a .303" land diameter, so it was called the ".303" rather than the ".312" or the ".3118".
The British used the same convention with the .280 Ross and the .280 British, which both have 7mm (.284") groove diameters and .280" land diameters.
The Russians did the same thing with the 7.62x54R. It has the same 7.92mm or .312" groove diameter but they also used very deep grooves with tall rifling with a resulting more diameter of .300", or 7.62mm. Thus it is the 7.62x54R, and not a 7.92x54R. The followed the same convention of naming I based on land diameter with the 7.62x39.
The Japanese followed the European naming convention with the 6.5 Arisaka round, which has a 6.7 mm groove diameter (.264") but a tall rifled .256" land diameter which is 6.5mm. Thus it was the 6.5x50mm Arisaka, not the 6.7x50mm Arisaka.
The Japanese were impressed by both the 7.92x57mm Mauser, and the .303 British. The Imperial Japanese Navy just created a knock off of the .303 British cartridge and called it the 7.7x56R, again referencing the land diameter, like he British, but stating it in rounded metric units. The Imperial Japanese Army adopted the 7.7mmx58mm Arisaka as more or less a slightly smaller caliber copy of the German Mauser round, using a .312" bullet like the Navy. Since it had a land diameter of .303" or 7.696mm, they just rounded up to 7.7mm when they named it.
You see the same in thnaming convention used in the 6.5x55 Swedish, the 6.5x54 Mannlicher-Schoenauer and the 6.5x52 Carcano cartridges. They all have a .264" (6.7mm) groove diameter, but are named based on a .256" (6.5mm) land diameter.
The European 7.65s are the also named the same way. The 7.65x53 Belgian Mauser has a .312" (7.92mm) groove diameter, but uses the 7.65mm name to denote the .300 bore diameter.
The 7.92x57mm Mauser, commonly called the 8mm Mauser in the US, has a .323" or 8.2 mm groove diameter and a .312" land diameter.
The parent cartridge for the 7.92x57 was the Patrone 88, adopted in 1888 with a land diameter of .312" and a groove diameter of .319" with .318" diameter bullets. Accuracy was poor so they changed the groove diameter to .323" to get taller rifling that would hopefully be more accurate (but strangely retained the .318" bullet). It wasn't any more accurate, but it explains some of the deeper groove/taller rifling efforts noted above in the 7.62x54R, etc.
The Germans redesigned the cartridge using the "S" type spitzer bullet. They retained the .323" groove diameter and used a land diameter of .312" or 7.92mm, and thus named it the 7.92x57 Mauser.
If you think about it, we also followed the same convention with the 6mm Lee Navy (.244" land diameter and .236" groove diameter),as well as with the .308" groove diameter cartridges like the .30-30, the .30-40 Krag, the .30-03, and the .30-06 which were all named based on their land diameter. We also call it the 270 Win, rather than the "277 Win".
It's only fairly recently that we started naming cartridges like the .270 .308 Win, .243 Win, .244 Rem, .223 Rem, etc based on their groove diameter. And you've probably noticed that we have our fair share of rounds like the .280 Rem, the 260 Rem, the 6.5 Creedmoor, etc, that are again named based on land diameter.
