I drive an 88 4+3 and I don't experience anything like this. I would not panic, however.
When was the last time you changed the oil and filter?
For the sake of discussion, let's just assumed that the OD unit is slipping, although I don't think that is happening since you say it is solid in other gears.
If it IS slipping the only thing it could be would be the clutches in the OD unit. If the time were to come when it is FOR SURE slipping it should be easily fixed. The clutches and planetary in the OD unit are just standard parts from some particular GM automatic transmission or another. I would be surprised if you couldn't find a competent automatic transmission shop that could fix it without too much trouble.
If it were come to that, you would just have to be careful to find someone who is a straight dealing shop. A crooked shop will either try to make you believe that it is something more complicated than it really is OR they will just take it apart and twist the steels so it won't slip long enough for you to pay them and drive out of sight.
You want to make sure that the shop uses new clutch plates and steels. No big deal at all. With the Vette it will probably be as much trouble to get the trans out and back in as it will be to replace the clutch pack.
Also, the valve body in the OD unit is super simple, but there could be something going on that is preventing adequate clutch pressure under specific conditions.