Another possibility, which may be off-the-wall:
The brakes are self-adjusting (threaded rod in a threaded cylinder extending between the shoes... the one with the adjustment star wheel on it) which is activated when the car is driven in reverse gear; I think those adjusters appear the same but they are right and left threaded depending on the side they will be installed, so It's possible the wrong adjuster(s) was installed (or they are reversed side-to-side) so that perhaps they are being tightened while the car is driven forward? I'm not certain if that is really a possibility, using the wrong adjuster may simply loosen the brake shoes.... but you can check to see if the right and left adjusters in your car are threaded differently and not the same.
If you have a Corvette Central catalog, the adjuster is #192009 and is listed as "L or R", which seems a bit strange since I would expect there to be separate part numbers; Dr Rebuild's catalog shows them as separate part numbers for left and right (5000174 lh, 5000175 rh).
As a separate issue, a bad power brake booster can sometimes reult in the symptoms you mention; in this case, letting the car sit awhile allows the brakes to return to normal operation, until you've driven a ways, whereupon they tighten up again.