You could probably get several hundred more miles out of it if the noise is when there is no load on the ring and pinion. I'm just guessing here, but might a thicker oil help?
The pinion could possibly be re-shimmed to take up the extra lash. Is yours the kind of axle where the differential comes out of the housing or does it have the cover on the back to access the gears? If it is the first, you could probably do it yourself. You could with the second too I guess but it wouldn't be as easy.
I'd recommend getting one, or more for spares, from the junkyard and swap them out. After you get one from the junkyard, you will know how hard, or easy as the case may be, they are to change. If it is simple enough, run this one till it blows up and then change!