Your fantasy gun does exist but at a fantasy price. Check out Krieghoffs new pump. It comes in 16 calibers including 7mm,300,338 mags also 375 and 416 ruger. Barrels can be swapped. I dont know exact price but rather than buying a new car you might want this.
In my humble opinion I think that there really wouldn't be much of a nitch for that type of gun. If you want one I do have a suggestion and it will be the Remington that you want. Get a 7600 chambered in .280 Remington and have that barrel rechambered to .280 Ackley Improved. It wil give you the ballistics of the 7mm magnum out of that pump. My only thoughts would be to check and see if the pump gun could actually take the pressures generated by the Ackley Improved. It would chamber in the gun and it would function from the existing magazines too. Now the other issue that I foresee is that Nosler Custom and some other semi-custom ammunition makers are the only ones that make factory ammunition for the gun. You would shoot those or have to reload. Just some thoughts. I know what it's like to have something off the wall that they don't make. Go for it!!
It might make to much sence for them to do. I think they have done some of the dombest things on caliber selection. How about when farris pendall and lou palmasono developed the ppc they took it to remington thought it would be a great caliber for there 40x, they turned them down.