I'm entering this discussion late, but I hope to make a contribution.
There are two kinds of Newton rifles. The first (pre-WWI) is an amazingly modern, well designed rifle. The second (post WWI), less so. The second model can be recognized instantly by the Enfield type dog leg bolt handle and the double set triggers, which face in opposite directions.
The first type has a safety on the side of the bolt sleeve which operates from front to rear. It has a straight bolt handle, low enough to clear the lowest scope mount. Both models have a unique takedown feature, by which the hinged floorplate is used as a wrench to dismount the front guard screw, allowing the barrelled action to be removed from the tang, which remains paart of the stock. Triggers and bottom metal remain with the stock also, allowing the rifle to be packed and carried in a case no larger than that used for a dismounted double barrel shotgun.
The .30 Newton cartridge was unique to the Newton rifle. What was later referred to as the .30 Belted Newton was simply someone's idea of giving an impressive sounding name to the unimpressive sounding .30/.338 Winchester.
It and the .308 Norma Magnum are practically identical with each other and the .30 Newton in case capacity and performance.
Comparative case capacity in grains of water: .30 Newton=89.20; .30/.338=84.41; .308 Norma Magnum= 85.78 (source: Handloader's Manual of Cartridge Conversions). As you can see, the larger Newton case should accomdate any load listed for the other two smaller cases, but I would proceed with caution, given the age of your rifle.
I have four Newton rifles, including a .30 Newton, which I have so far not shot. Two of the other three are .256 Newtons, which I have shot a good bit and am quite pleased with. The similarity of Newton's cartridge to the .270 Winchester should be obvious.
Newton was a firearms innovator, responsible for the design of the .22 Savage Hi-Power, the .250-3000 Savage and the .300 Savage, all radical improvements over their contemporary cartridges. The .256 Newton was an attempt to make a commercial cartridge out of the .25 Niedner, which was simply the .30-'06 necked down to .25 caliber. Newton's German barrel makers were not set up to manufacture .25 caliber (.257") barrels, but they could supply 6.5mm (.264") barrels, which Newton chose to refer to by their bore diameter (.256").
Many of his rifle features were incorporated in the Model 70 Winchester when it came on the market in the 1930's. Unfortunately, his business skills did not match his innovatation and he was jinxed by the outbreak of World War I, just as he was getting his rifle business started, which cut him off from his German barrel supply.
I think you will enjoy your .30 Newton, but I also think a more robust stock than the one originally furnished might be called for. The recoil may be more than the stock can stand.