Hi, John I am now in the process of replacing my own terrazzo base for the exact same reasons you stated.
I asked around and decided to just take this out and replace in kind as it did give me great service and it also lets me redo a bathroom at the same time.
If it is a preformed base by Fiat or similar, by the time the surface reaches the state yours has, the metal flange around the perimeter is usually rusted away. Replacement is the best solution.