SP2 , the 375 2 1/2" is a sreight sided case similar to the 375 Winchester! Cases can be made from 405 Win, by simply running them in the 375 2 1/2" dies, and trimming to length.
This is a deer cartridge, and factory ammo pushed a 270 gr lead bullet at 2000 fps, for a muzzle energy of 2400 fpe.
In a double rifle chambered for this cartridge, I would not axceed the factory pressures.

I have seen the rifle you are talking about, I think, and it is a nice looking rifle, if someone polished off the stupid blueing sombody did on the action. The action was origenally case colored, but would look much better polished to a coin finish. That dealer can do that for at a fairly low cost. If it is the same one, dies, and some brass comes with it! It would make a nice woods, or brush country deer or moose rifle! It also would make a nice double for the moveing target double rifle shoots that are becoming popular as of late! The cartridge is obsolete, and has been for 100 yrs.