O.K., since no one else remembers, here is an alternative to your dilemma:
Heavy Express
The HE MAG line of Magnum Cartridges are also based upon the .348
Winchester casing with the rim removed and blown-out to Improved dimensions with a 40 degree shoulder angle. HE MAG cases come in 2.25 inch lengths for Standard Action rifles in Calibers .338, .350, .375, .416 and .460.
HE MAG cases have .530 rim diameter, .545 base diameter, and a .515 shoulder diameter making these minimum body taper cases the most efficient case design in production today. The only exception to these case dimensions is the .460, which has a .526 shoulder diameter with a 45 degree shoulder angle. Cases are commercially manufactured for Heavy Express, Inc. by MAST Technology, Inc. of Las Vegas, Nevada. Heavy Express Custom reloading dies are manufactured by Hornady Manufacturing Company, Grand Island, Nebraska.
And:
The Heavy Express range of cartridges was developed by Jim Busha, from Colorado Springs CO, and was based on the 348 Winchester case with the rim removed. They came in a variety of calibers,
ranging from .240 to .500 caliber and in 2 different versions, namely the "normal" length (Heavy Express) and the shorter length (Heavy Express Short Action Magnum). These can almost be argued to the forerunners of the Winchester Short Mag and Winchester Super Short cartridges.
Now before anyone goes off the rails because they notice that the rimmed .348 Win. has been changed, this was a common adjustment to rimmed cartridges used in rimless actions. It takes a lathe and a little ingenuity for making the tooling but it's relatively easy for a conversion.
Enjoy the thoughts!