I changed oil at 1500 miles on my Z. Oil came out very clean. Also, I inverted the oil filter to check for debris, as in metal shavings, and found none even after running a magnetic rod in it. Another option for car owners is to have an oil sample sent off for analysis. I used to do that after an engine rebuild just to see what was wearing. Its amazing what they can tell you from the oil analysis.
Overfilling an engine causes the oil to be beat by the crank and rods in the lower assembly. In the case of a dry sump system like the Z's, its obvious the oil reservoir won't hold too much more than 8 quarts but I can't see how having maybe 4 more quarts resting in the bottom of the engine pan could make the crank foam up the oil that quickly, unless they ran it for 20 or 30 minutes. Obviously it did or there wouldn't have been smoke. Greatest damage is likely the action on the cam lobes due to the pressure area. Second would be the rod bearings, with the main bearings being the least affected if the vehicle was at rest or just idling. If there was damage, it will surface in the next 500 miles. The good thing is that synthetic oil leaves a good coating on metal parts like the bearings and cam lobes. The other good thing is the car has a 5 year, 100,000 mile warranty.
The bad thing is the car is brand new and very special to its owner. Its kind of like having your new car get slammed by a car door in a parking lot. That first scratch is like a sword going thru your heart. That dealer doesn't sound like they cater to Vette owners very well, and likely don't really give a crap about your car being a Z. Find another dealer or do the minor stuff like oil changes yourself. Also, if you use a trusted auto service shop for your other cars, why not trust them for the non-warranty work on your car ? You are more likely to be dealing with the owner of the shop or another family member, and they rely on repeat business and long term relationships. The dealer doesn't, regardless of what they say.