If I remember right, those old short action caliber rifles that were manufactured on a long action receiver have a different bolt head on the bolt that limits rearward travel of the bolt when cycling the action that might even add another layer of nope to the equation.
In addition the .300 RUM magazine as well as the action cutout is even longer than the standard magnum calibers so if you want more than a single shot, even on a rifle that came from the factory as a magnum, some machining will most likely be necessary. Another thing that comes to mind, I'm pretty sure almost all of the factory produced .300RUMs were built on large shank actions.
Basically if you want an RUM it's probably most economical to buy one.

On the bright side, the bolt head, small shank action, and magazine that you have are the most common sizes so if you want to swap barrels to something with a little more thump like a .308 or a .338 Federal (I've read it's supposed to be close in energy to a 7 mag) It's entirely doable with nothing more than a barrel swap.
Good luck