To me it looks like the chamber area of the barrel is shorter than normal. It could easily have been set back enough to clean out the existing chamber. I used to have a couple of the Westinghouse Mosins that were converted to 30-06. They were set back as well. The only other thing different about the two I had was they had and extended extractor. They also fed from the existing mag without issues. If I hand loaded for them with 312 bullets, they shot very well.
There was a lot of hype about these actions not being strong enough for the 30-06. IMHO those comments were put out by writers that had no clue as to what they were talking about. Similar to those that berated the Japanese Arisaka actions.
IMHO, the rifle is plenty strong enough to handle the 308 Win round. Of course that is my opinion and you should do your own. The 7.62x51 Nato round which is dimensionally identical is usually loaded to slightly lower pressures than its commercial cousin.
It's pretty easy to make up a simple chamber cast out of plaster. Spray a bit of cooking oil or some other sticky lubricant into the chamber then plug the barrel with cotton batting or something similar. Place the muzzle in a downward facing position and pour a bit of plaster into the chamber and let it sit overnight. DO NOT CLOSE THE BOLT. In fact, pull the bolt or you will have to strip and clean it as well.
Plaster will not give you the exact dimensions but it will be close enough to make sure what the cartridge is. I have seen plastercene and silly putty used for this as well using a similar method of release but it can be easily pressed into the chamber by hand and then chilled to freezing or close to it and tapped out with a cleaning rod from the muzzle.
