Eric, first is using the right glue for inserts. I have had very good luck with the Bohning Powerbond product with shaft damage due to insert pushed into it dropping to a rarity. I know some others have done well with glue specifically for graphite golf shafts.
As far as repair, sinew works great! Pull the insert if you can and wrap it tightly, reglue the insert in. I know Charlie Lamb has a couple resurrected like this that are still going strong...maybe stronger than before.
Other guys have gone so far as footing with an aluminum shaft over the carbon. I've not done this myself, but hear it makes the carbon shaft almost truly indestructible.