Well I'm a little conflicted on this one.
It is starting to sound like a bad sending unit.
I know of 2 ways to test:
1) pull the sensor out of the block and put in a buck of hot water and see how the gauge reacts. If the water is 200 degrees (be careful you don't burn yourself) that is about operating temperature, so you can see where the gauge points.
2) buy an ifra-red thermometer. The are the hand held devices that you point at something and it tells you the temp. They are about $75 at Sears. Get the engine warm up and then point the gun at the thermostat housing.
It could still be the radiator.
When I bought my '82 the radiator had been "fixed" with a can of sealant. It fixed the leak and plugged the radiator solid.
It would overheat if you let it idle too long.
Then I replaced that with a light duty radiator. That was ok at idle, but would run over 240 (I love that the C3 gauge has numbers, not "lo" and "hi") in a normal drive. It would be at 260 at highway speeds.
Then I replaced that radiator with an aluminum one from DeWitt's. Now I can drive up hill at 75+ mph with the AC on when it is 100 degrees, and my temp barely touches 220. I'm not exaggerating.
What you're describing sounds a lot like my early problems: ok at idle, but gets too hot, too quickly.
Are you sure the water pump is working?
A lot of pumps have an aluminum shaft and propeller.
If they corrode, the propeller breaks off from the shaft.
As a result, the belt is only turning the shaft. The spinning shaft can cause enough rotation and flow that the car will "burp" the air out of the system, but not much else.
Unfortunately, the only way I know to test this is to remove the water pump and look at it.
See what the radiator shop finds.
I'd also get the IR thermometer. That's the only way to know if the car is as hot as the gauge indicates.
Craftsman Infrared Thermometer (i'm not endorsing this, it is just an example of what I'm talking about).
Good luck, thank you for the compliment, and I hope you get back on the road soon. Corvettes are fun to look at in the garage, but more fun to drive!!!