Do you have a basement or crawl space where you have access? That will determine how easy it is to replace that part with plastic. A plumber could lead a new flange on and break off the excess...not sure I'd attempt that as a DIY'er though. Ideally, the new flange would go on TOP of the finished floor and anchor through it into the subflooring. To make it easier to anchor if you are going to tile, notch the tile where the screws go so you don't have to drill through the tile.
Depending on the subflooring, and the kind of tile you choose, the joists may or may not be stiff enough to support a tiled floor. Check out www.johnbridge.com for some help on that front...once there, look in the blue bar on the forum for "Deflecto" which is a stiffness calculator to check it out.