This, was done in the 1920s in Britain and by O,Neil, Keith and Hopkins about the same time.....largely what inspired the superb .338WM.
Yup the cartridge was part of the OKH line of cartridges developed by Charlie O'Neil, Elmer Keith, and Don Hopkins in the 30's. The 334 OKH was based on the 300 or 375H&H case necked to .333(British caliber) and drove a 250 gr bullet about 2800 fps.
It had a shoulder and long neck.
The cartridge also had a little brother in the form of the 333 OKH based on the 30/06 case;and later another called the 333OKH belted which was shorter than the 334 and much like the 338 WinMag.
The 340 Weatherby is nothing more than a necked down and blown out 375H&H case; it is also just a 300 Weatherby case necked up,Both derive their origins from the 375 and 300 H&H cases.
So a 300 H&H necked up today is not going to do anything a 340 Weatherby won't do. It's a very old concept and OKH did it all years ago.