Put it in a box, then get a new one
Guy, a water pump can wreck your whole engine.
One member or more had them come apart and trash half the engine bay.
This is not to mention not cooling your engine in the meantime.
You have a lot of options in either iron or aluminum high flow versions you can make look original that are much better than anything the General put out in the late '70's. (I think the tiny weight savings of aluminum vs. steel is almost irrelevant in a sports car on a water pump, but not so corrossion, appearance or some heat dissipation. I tend to think the cast iron is stronger than aluminum, but am not sure on these 0.75" bearings and with the decent grades of cast aluminum Edelbrock, FlowKooler (sic), Milodon and the others use.)
Now whether new or rebuilt is really irrelevant, exept for the specs of some of the new ones. But I would not rebuild yours, yourself.
I went back and re-read your post after I posted: if you have a decent service that takes your water pump and rebuilds it with new seals, bearing and impeller, then this would certianly be OK. I'd still put on a decent unit while you were waiting for that to be done, since I imagine there is some time involved. Perhaps they can put you in an upgraded impeller (not that impeller design is like, super-magical or anything.)
That way you can use your car while waiting for it to be perfected. Water pumps are cheap and easy to change on a SBC.
Additionally, several good pump makers make an improvement kit to change your stock WP design from an undirected open impeller design to a more efficient semi-closed impeller one. I would normally be leary of drilling holes in an impeller and non-hot rivetting some addition to a thing that gets beat up like a water pump, but since it comes form people like FlowKooler, it might be worth considering.