The ejector (which is pinned into the left side of the receiver) is located closer to the chamber on the 2 3/4" model 870 than the 3" Magnum model. So the mouth of a 3" fired hull will not clear the ejection port when the ejector tries to kick the fired hull out through the port.
Your shotgun will fire 3" shells with the 3" chamber full choke barrel attached. But it will function like a single shot. You'll probably have to remove (or at least loosen) the 3" full choke barrel in order to remove the fired 3" hulls.
A 3" Magnum 870 ejector can be fitted to your 35yr old 2 3/4" receiver. But it will cost $$ and the left side of the receiver will look boogered, after removing the existing pin and ejector, and installation and re-pinning the Magnum ejector.
I've done this ejector replacement on one of my 20ga 870s. Converted it from a 2 3/4" receiver to a receiver that now functions like a 3" Magnum receiver.
If you gotta hire a gunsmith to replace the ejector, I wouldn't do it. The new ejector isn't too expensive, but gunsmith time and labor will be. And even then, the finish on the left side of the receiver won't be as nice. Remington installed the ejector, pinned it onto the receiver, then finished surfacing the exterior of the receiver, and then blued the receiver. Done this way, the pin that holds the ejector is barely visible on the receiver. Removing that pin and installing a new pin on the finished receiver..., the pin will be pretty visible.
I recommend buying a used 3" Magnum 12ga model 870, if you're dead set on shooting 3" Magnum shells.
