If you want to save money on oil changes, then by all means use a good synthetic oil and change it less often. 3,000 mile oil changes are a myth, you can easily go 10,000+ miles up to 25,000 miles with synthetic oils like AMSOIL. You will want to use one the meets GM high performance oil spec GM 4718M. Most synthetics mention GM 4718M in their list of claims; that's the unique spec created by General Motors for Corvette oil. It's a high-temperature requirement that tolerates less oxidation (thickening) and volatility (boil-off). Avoid bargain synthetic oils. Not all synthetic oils are made the same, you get what you pay for.
GM factory fills all Cadillac with synthetic oil meeting GM Spec 4718M. All Corvettes since the 1990's come with synthetic oil and more and more cars are requiring it.