In Mr. Ackley's books, available from eabco.com, sinclair, ebay sometimes, etc.; there is a summary of thousands of cartridges, factory, improved and wildcat.
Remington was making a bad joke with the .350 Mag and the 6.5 Magnum -- a belted case short enough for a pistol action, the XP100 pistol and Model 600 rifle as I recall. The magnum head came from the H&H family which were, in the earlier times used to get more powder capacity into full length actions--larger in diameter than the .30/'06/Mauser family of cases,in the 1917 Enfield especially. And blown out. To shorten the belted case when the .308 case and .358 Winchester was already on the shelf... Not that funny, not that useful...
Reportedly the .300 savage was tried for the military cartridge and the .308 was the .300 Savage with more neck. I suspect someone took the .300 Savage up to .358, although with the short neck... lame.
Working with the .350 Case is not going to be alot more fruitful. With the .308 family out there, why? No doubt if you look far enough, you will find something, but with the cheap surplus brass in .308 (sorry 7.62 X 51MM NATO) not alot. luck