The 1969 Gun Digest contained an article by Chuck Hagel with extensive discussion and load development of the .338 Win, the .338/300 Win Mag and the .340 Weatherby. The .338-300 does indeed have more case capacity than the standard .338 Win Mag.
Hagel had loading data for the .338-300 Win Wildcat. He used an M-70 full length action and rechambered for each round or re-barreled as may have been the case. His big deal was to "long throat" the .338 Win and .338-300 so that bullets could be seated with the base of the bullet flush with the case neck. The 338-300 was, as I recall, right in between the .338 Win and the 340 Wby. By "long throating" the .338 Win Mag, he bumped up speeds another 100 fps. Elmer Keith did this too, using a full length magnum mauser action with his .338 Win Mag and long throating and seating out the Speer 275 Grain Bullet.
I did this with a .338 Win mag so that cartridge OAL was equal to the .375 H&H and I was getting 2,850 fps. with the 250 Gr. Nosler partition bullet. I bought the rifle with the intention of rechambering for a .340 WBy, but frankly the recoil with the .338 Win was as grim as I could stand and I could not see where another 100 or so fps provided by the larger .340 Wby would make any practical difference.
I don't know what you're going to do with the rifle, but personally I would stick with the regular .338 rather than fiddle around with necking up the .300 win mag case. Maybe I'm getting to old for this kind of thing, I don't know. You're talking about re-boring an existing .300 win mag. The last time I priced this type of thing, re-barreling was only slightly more expensive. Personally that's the way I would go. Every time I read some book and get a bug up my behind for some weird off the wall deal, I end up spending a lot of money and end up with something that is only marginally superior to what I could have bought right off the shelf. Frankly if the .338 is not enough gun, you should probably go for the .375 H&H.