Get the mice out and repair whatever damage they may have caused. I assume you're already doing that.
Putting moth balls around the car port is a little messy as they will blow around. Put moth balls in the Vette, under the hood. Anywhere the mice like to be.
Keep the grass mowed around the car port so the mice have no place to hide.
You might want to put the Vette back in the barn and make sure all mouse holes and other access to the barn are sealed. Moth balls will work better in the barn also.
Years ago, I found mice in my old C4 that I parked in a barn. After cleaning out the air box (air filter) and the spare tire well, I 'sealed' the barn with spray foam and put better insulation around every door. That make it much harder for the mice to get to my car. I also mowed the grass around my barn more often.
You could surround the outside with mothballs, but put some fabric softener dryer sheets inside the car and engine compartment.
I would have to disagree with putting mothballs inside the car. I've see pre-owned Corvettes come in on trade at a local Chevy dealer, and the inside smells like moth balls. It's difficult to get the odor of them out of the car.
You'll not only keep the mice our of your Vette - you won't want to spend much time inside of it as well...
We've been using this stuff in our 5th wheel for years (stored outside all winter) and it works well for us. The smell isn't offensive at all, sorta likea balsam pine odor. Most any rv store will sell it. I've seen it at home depot, too. And, I also throw a couple in the engine compartment of my Jag as it sits in the garage all winter.
Arizona, in the winter months, sees a host of packrats and woodrats searching for a place to hide from the cold and a great many like hiding in the engine compartments of our cars. They like to eat wiring and will search for a way to get inside the passenger compartment as well. I had to replace the A/C harness on my '07 Silverado in the first winter so I looked, like you, for a mouse cure. Their point of entry starts with the tires, which they climb. My truck sits in the drive as the garage is full of toys so I spray the tires after a rain or once a week with household ammonia with half a bar of Irish Spring in it. In the 10 years since I started using that foul smelling mixture, no packrat damage.