Does anyone have suggestions for repairing the screw holes that hold the center guage cluster in place? I did some seal replacement in the air distribution system and I'm concerned about the plastic on these original pieces.

Peter, what happened broken out pieces, or bad threads?

Threads you can push epoxy into let it start up then coat the screw with cooking oil and screw it in until it dries.

That works really good.  I have done it that way but not on my Corvette.  I can also tell you what does not work and that is a big list. 
Another thing you can do if you can get to the back where the screw are going to go in and that is get some soft plastic or even rubber about 1/4 thick and clue it to the back.  Hot glue works good for this and then use a screw long enough to go through it all. 
You can also us Hot glue instead of epoxy same procedure.

Just bad threads. Thanks for the suggestion.

I have cut one end off a paper-clip and placed it in the whole. The screw will bite into the paper clip so no need to locate larger screws or "doctor" the hole.